Air carrier Flight Attendant reported high cabin air temperatures during single-pack flight operation resulting in several passengers experiencing discomfort and physiological reactions.

Narrative

The inbound crew on flight ZZZ [airport] to ZZZ1 [airport] wrote up a broken pack upon arrival. Maintenance working deferred it in order for us to work a flight back to ZZZ (& likely a flight onward to ZZZ2). (I have worked with deferred packs before; but never on a former dual cabin-control aircraft which would prove significant & problematic the remainder of the day.) Flight back to ZZZ proved uncomfortable; but not unbearable. After the boarding was closed; I made an announcement & explained the deferred pack ('Down to one air conditioner instead of 2'); apologized for the discomfort that would follow; and asked passengers to open their air vents. We sat at the gate after departure without engines running; waiting for international baggage to arrive which added to the general 'stuffiness'; but once airborne the temperature fluctuations from a single operating pack seemed to alternate between the forward and aft cabins with enough regularity that neither part of the cabin grew outright hot. It was a short; XX-minute fight and passengers dealt with the discomfort in order to get to their destination: layers removed; air vents open; water served.Prior to boarding the flight to ZZZ2; I spoke with the ZZZ gate agents to explain the cabin temperature situation; request a hard cut-off at XX carry-ons to ensure overhead space would be available to allow passengers to remove & stow layers & personal items - to make themselves as comfortable as possible. (A XX-minute flight in a poorly ventilated cabin is one thing; X hours was going to be quite another.) After the boarding door was closed and just prior to closing the flight deck door (FDD); I mentioned to the CA that I would make the same announcement I had made on the previous flight and continue keep the pilots advised of the cabin temperature. I then said; Cabin secure for taxi;" and closed the FDD. Almost immediately the CA popped open the FDD and "asked" me not to make that planned (& previously-given) announcement regarding the pack and cabin temperature because "it might draw complaints".This request did not sit well with me. After the safety demonstration; in lieu of making an announcement; I walked through the cabin; stopping every 4 rows; to say; "Controlling the cabin temperature will be difficult this evening. I suggest removing outer layers & opening the air vents above your seats. We will be in the cabin throughout the flight to assist you." I stowed jackets & assisted with air vents.Within the first XX minutes of the flight; cabin service was delayed due to Moderate Turbulence warnings from the fight deck. Flight attendants returned to their jumpseats for XX minutes per the CA's request. B-FA (Flight Attendant) wondered if she should conduct a water/snack service only; I rejected that idea. Given the cabin temperature situation especially; it was important to work with the smooth air we had for as long as we had it and take care of the main cabin. (She could always stow the cart if we encountered significant turbulence and continue with a hand service.) After the XX minutes; we proceeded as normal.I conducted the First Class cabin service (X Seltzers; X Scotch Rocks; plenty of bottled water) and moved to the Main Cabin to assess the temperature/comfort level. I found a wall of heat beginning at Row X and extending to Row Z. This dissipated only slightly as I moved through the back half of the Main Cabin. I notified the Flight Deck of the extreme heat and then grabbed a cup of ice water and packs of wipes and began distributing 'cold towels' to passengers while the B-FA conducted the beverage service. Passenger A had boarded feeling nauseous with an empty stomach & requested cookies which I immediately provided. I monitored Passenger A throughout the flight. Passenger assured me they were 'fine' (all things considered) once they had something - cookies & Chips - in their stomach. Passenger B (traveling with Passenger C) suffered a panic attack due to theextreme heat roughly XX minutes into the flight. I advised B-FA to provide an ice pack and cold beverage. I found Passenger B breathing into a container as a precaution for nausea. I provided 'cold towels' & additional ice water & monitored Passenger B throughout the flight. Flight attendants continued to monitor both cabins (the only complaints in First Class were of spotty WIFI) and dispense water as requested. The flight deck was also kept informed. The cabin temperature only stabilized twice (about 10 minutes at a time) and did not cycle or alternate between the forward and aft cabins as it had on the previous flight. This meant that passengers sitting in Rows X-XX were outright hot for the majority of the flight.Passenger D (and a Passenger who had swapped into another seat) asked during descent of the airline would provide compensation for everyone. I asked Passenger D to provide feedback and assured I would do the same. Upon arrival at the gate; I notified a Gate Agent that the flight had been incredibly hot & passengers would complain. (I also warned her they might chase her up the jetbridge just to get to fresh air & AC.) I spoke with her again after deplaning to explain the full scope of events; ask her to note any complaints; and note a blanket request for some sort of compensation. She assured me she would do so as well as escalate to a supervisor. She voiced her shared concern that this flight could have involved a medical diversion with multiple passengers and let me know no one complained about the cabin crew's response to the situation only the "unbearable" heat. During Deplaning; an unknown Passenger E complained; 'We should have been given water. That was unbearable.' The two other passengers immediately behind Passenger E looked at me; rolled their eyes & shook their head. (In addition to the scheduled full beverage & snack service in both cabins; we were in the aisle with water throughout the flight. I had also repeatedly walked through with ice water & wipes offering 'cold towels' to help alleviate passengers' discomfort.)Passenger F was the last to deplane & shared; 'If you all knew (this was going to be an issue); we should have been given the option to take another flight.' I did not disagree with Passenger E and asked them to share their feedback. Passenger E informed me they already had; but was 'only' offered a travel voucher.Suggestions: The first X rows of the aircraft (particularly First Class) were never as hot as Rows X-XX. (Rows X; Y; & Z were the hottest - a veritable hell at times. Rows A-XX best described as a sauna without the humidity.) The forward cabin was uncomfortable and stuffy; to be sure; but they did not suffer from direct heat as the mid- and aft cabin. First Class seemed satisfied with bottles of water and seltzer which allowed me to focus attention on the Main Cabin. To the extent that we knew regulating cabin temp & pressure would be an issue; we knew it was going to be…uncomfortable. We did not know the extremes to which the temperature would rise or the wild inaccuracy of the readings on the flight deck. (I was advised after the flight that the cabin temperature reading never rose above 22C/77F; but the reality was much; much hotter.) The former aircraft in the fleet; however; are the only tails with 2 dual-zone cabin-controls and are notoriously difficult to manage when both packs are operational - never mind when one is deferred. (I have described them as "menopausal" in the past.) That aircraft should only have been flown the one leg back to ZZZ and grounded until Maintenance could repair the pack. Poor CRM was a major exacerbation. I did not appreciate being 'asked' by the CA to avoid addressing the imminent discomfort lest it 'draw complaints'. Knowledge is power; as they say; and acknowledging an impending issue; apologizing for it; and suggesting 'solutions' (such as removing layers & opening air vents) all help to mitigate customer dissatisfaction and avoid outrage. I understand pilots' general 'I could never do what you do' attitude towards customer service & dealing with passengers; but at the end of the day; the passenger appreciates the acknowledgment & mitigation - puts more weight on words voiced from the Flight Deck (The CA's silence and outright avoidance proved to be deafening.) Hearing the CA say; 'I didn't realize it was that hot. They're pissed!' after Deplaning ('Yeah!'; was my reply.) caused me to reevaluate more closely what I might have done differently given the situation - a PIC wanting to avoid complaints; an uncontrollable cabin temp; and a XX passengers on X-hour flight.In lieu of a standardized vocabulary and unreliable temperature readings & dials; I could have been more descriptive to convey the severity of the situation: "Row X feels like you've opened a 400-degree oven and stepped inside."I could have invited/suggested a pilot walk through to the rear of the cabin to better understand what we were dealing with."