Embraer 145 Flight Attendant reported a hot cabin with passengers suffering after a maintenance delay and passenger loading discrepancy. The discrepancy was resolved and the flight departed for the destination.

Narrative

The aircraft was on a long maintenance delay due to indicators that came on during the unbound which could have detected the fuel was corrupted and not pure. Not being a maintenance base a non-Company mechanic needed to be called. It took a while for him to arrive; and to run all the diagnostics and clear the aircraft for operation. during the last fifteen minutes of the delay; the gaspers started blowing hot air.We were being cleared by maintenance; and the agents were anxious to board and be relieved of the difficult task of managing the customers. the temps in the back on my unauthorized thermometer was above 91; but the flight deck indicator only registered 72; not constituting a hot plane. The decision was made to board quickly and get the already greatly inconvenienced faster out of there to the hub. Unfortunately; my accurate count was 34+ an infant. Often the gate agents do not have a uniform way of communicating the amount of humans on board when there is a lap child involved. Having had several encounters with this over the summer I verified with the gate agent that the written and circled 35 on the final paperwork was 34+ an infant was correct; there was a little bit of back-and-forth; but I knew the amount of people on the plane so I again asserted that it was 34 seats plus one lap infant equaling 35. The account matched with the flight deck and the door was closed; however; during my announcement prior to the safety demo; the flight deck called and asked me to verify the amount of persons in Section X. Apparently Section X had the correct count; but after the door was closed; and the agent went back up. They added another person to Section X. This became problematic and the door had to be re-opened. The passengers were already extremely hot; but bearing up in order to have an on-time departure and looking forward to cooler air once airborne. But unfortunately; at the door came open; and the heat situation became unbearable as the gate agents called out names and made a roll call. I was during this time that one woman who was a wheelchair passenger and aged 82 was not doing well and had to be brought to the front. A young service man went back and took a seat in her section for those weight and balance purposes. Initially EMTs were on their way; but the woman said she felt much better in the front and did not want to be removed from the plane. The beginning of this flight was miserable; and the people were very angry. By the end of the flight; most of them had calmed down and had a strategy for their connections. However; the plane was unsafely; hot and for an extended amount of time. It was difficult to think. Old planes; a summer filled with horrible heat and horrible delays; and a non-standard way of listing the final count when there is a lap child involved-I have seen several different ways of communicating the final count; and have had to at least clarify. Company issued thermometers for flight attendant to use at out stations; and language in the manuals to allow for accurate readings to be addressed appropriately. No more flying hot planes.