A319 Captain reports refusing an aircraft due to an inoperative APU and ambient temperatures in the mid nineties.

Narrative

It was about 95 degrees in the departure airport and the next two destinations; and the assigned plane had APU inoperative. After discussion with the First Officer; we decided to refuse the plane. The Duty Manager called me a few minutes later; and asked what the problem was. Say what? I answered that the plane was the problem. He then asked if the problem was with not having the extra APU generator. Come again? He knew exactly what the problem was; and I felt like he was trying to manipulate me into saying words or phrases that the company could later use against me. The First Officer went to the plane in question and with ground pre-cooled air and no passengers on board; the cockpit was 94F and the cabin was 96F. Again; that was with pre-cooled air pumping into the plane! With a full load of people and air removed for 15 minutes before push; it would have reached 120F easily! It never would have cooled during the 1 hour flight. The A Flight Attendant stated that she was feeling like she was going to pass out and was uncomfortable taking the plane. We also had a group of special needs passengers; some of whom were in wheelchairs. My experience tells me that there were also a host of unknown medical problems in the group. They didn't need to sit for 40 minutes (boarding and taxi out) in 100+F temperatures. Is this how we treat our employees and passengers? I feel like the Union code of Ethics demanded that I refuse the plane; and I now feel 100 percent in the right the next day. Maintenance and management failed me; my crew; and my passengers.