B747-400 Captain reported they returned to their departure airport due to an inoperable transponder and a crewmember illness.

Narrative

Following a customer caused departure delay; we experienced an air turn back in ZZZZ due to a transponder malfunction and a cabin crew member indicating they were overheating/becoming sick due to overheating. Upon arriving at the aircraft; it was conveyed to the crew that we would be delayed due to the customer having issues with manifesting/clearing their outbound passengers. The aircraft was already very hot (38-40C in all zones with lower decks at 50C/47C respectively) with the APU running and all 3 Air Conditioning Packs running. Maintenance informed the crew that there had been a cooling cart hooked up previously; however it was blowing hot air so they switched to the aircraft AC packs to try and keep the aircraft cool (time was approximately XA15 ZZZZ). After briefing the Cabin Crew 30 minutes later; I (pilot in command (PIC) was informed the delay might be extensive and that some crew members were starting to feel the effects of the heat. A few moments later; upon returning to the flight deck; we discovered pack #3 was not working properly; alerted Maintenance; and left the flight deck while they worked the issue so we could check on the cabin crew. After checking on the cabin crew members; reminding them to keep hydrated and to try to find cooler spots on the aircraft (galleys) I conferred with the pursers who suggested we try to get a crew bus with AC to wait out the delay. They contacted the station personnel and I called the Duty pilot to alert him/see if he could push from his end for the bus. I next called our Dispatcher to inform him of the delay.A short time later; the bus arrived; the cabin crew and flight deck crew went to the bus to cool off. Eventually we got word the issues were resolved and the passengers were ready to come to the aircraft. We boarded the aircraft; prepped for guest boarding; checked with maintenance on pack status; boarded the guests; finalized our departure preparations; briefed the departure and consulted the duty pilot for a potential duty day issue. After clearing up the latest allowable takeoff time issue with Supervisor's assistance; I consulted the flight deck crew and granted PIC concurrence to extend the FDP (Flight Duty Period) by 2 hours under part 117; so we could depart. We subsequently blocked out at XA55 and commenced takeoff at XB19.Climbing through approximately 1500 ft. we received an EICAS message of '>TCAS OFF'; indicating the collision avoidance system was not working properly. Shortly thereafter; Departure Control inquired about the status of our ADS-B transponder as they were not picking us up on radar. After reaching a safe altitude; we referenced the checklist; checked circuit breakers and attempted to switch transponders (L/R) as well as switch transponder modes with no success. ATC cleared us to fix ZZZZZ and cleared us to climb to 22000 ft. while asking us multiple times to check our transponder. I inquired if we would be able to continue and they replied that they were already checking with the next airspace sector. Approaching ZZZZZ; ATC issued holding instructions at ZZZZZ at 22;000 ft. We entered holding (approximately XB30); leveled the aircraft; I assigned flight deck crew tasks for the First Officer (FO) to fly the aircraft and monitor ATC frequency with the relief pilot monitoring ATC/SATCOM and the FO from the jump seat; while I contacted the company on SATCOM to try and determine decision fuel/time; sort the issue/see if we missed something and determine an appropriate course of action (while thinking/hoping the transponder was just possibly overheated and might start working once the airplane cooled off). The Dispatcher; who was excellent throughout assembled the team of maintenance and the Duty Pilot to discuss the issue. While the team was trying to be helpful; the question came up as to whether we considered 'cycling the circuit breakers' for the transponder. I answered no; and that I would not consider doing that as an option; since it isnot part of a procedure and per our QRH that the flight crew cycling (pulling and resetting) of a circuit breaker to clear a non-normal condition is not recommended; unless directed by a non-normal checklist. During these discussions there was also a knock on the flight deck door and a call from the upper deck cabin crew that there were maintenance personnel waiting outside hoping to possibly assist us on the flight deck. I asked them to have them return to their seat as we were not requiring their assistance in flight and were already in contact with Company Maintenance on SATCOM.In the midst of the discussions; I was informed by the purser that we had a cabin crew member experiencing symptoms of being sick with a heat related issue. I was told the crew member was seated; being given water; a cold pack and that they did not think MEDLINK assistance was necessary at that time. I completed the briefing non normal communications protocol with the purser; passed this information (sick crew) to Dispatch and shortly thereafter; we came to the conclusion that an air turn back would be prudent since we could not continue per ATC and now had a potentially ailing crew member. Dispatch sent us a reanalysis for the return; I next circled back to the purser to discuss our ailing crewmember and assess the status of the guests/crew. The purser informed me that our crew member was still seated; but doing better; they requested some time to finish a meal service for the passengers and we discussed cooling the cabin as much as possible before the recovery into ZZZZ so as to avoid more heat issues on the ground. Since we were overweight for landing; I elected to give the time by burning the fuel to a landing weight in a holding pattern while we configured for the arrival and cooled the cabin as much as possible (still over 30C after over 1 hour airborne). ATC relocated us to a different holding pattern over point ZZZZZ1. While holding at ZZZZZ1; the cabin and flight deck temperatures dropped below 30C and the transponder began to operate intermittently at XC05 with ATC finally identifying us at XC15. We burned the fuel to landing weight shortly after being made aware the cabin crew was ready for the arrival and requested the arrival for Runway XXL to minimize taxi time to parking/further heat exposure for the crew. We descended in holding; were given extended vectors and eventually completed an uneventful landing by the PIC at XD20 with block in at XD31.Uncontrollable customer delay; exacerbating a poorly planned departure time; compounded by an air conditioning cart heat soaking the aircraft in the middle of a very hot (46C/114F) day; resulting in the on board air conditioning system's inability to adequately cool the aircraft. Departures from desert locations should not be planned for the middle of the day during the summer. Departures from these types of locations should be planned/scheduled for late evening/early morning (dark) so as to mitigate potential heat related issues with crew and the aircraft. Next; Duty pilots need to be reminded that cycling of circuit breakers is not an appropriate recommendation to make to crews with an in flight abnormality unless it's part of a published non-normal procedure. 'Not recommended' does not mean there is 'wiggle room' and stating such (that there's wiggle room) could put undue pressure on a stressed/newer/younger/less experienced PIC to assume an undue risk because they now feel pressured to do so. This runs contrary to Flight Crew Operations Manual (FCOM)/QRH procedures and could be dangerous/unsafe in certain circumstances. Lastly; while well intentioned; maintenance personnel should be made aware that accessing the flight deck or requesting flight deck access in flight is not an appropriate action for them unless specifically requested by the crew. There are no airborne activities they can perform or are certified to perform short of advising the crew; which could be accomplished via phone from the cabin; if required.