Inferring we have no consideration for passenger comfort is toss. I have wandered after ground crew on a number of occasions to get them to plug the air con in, and it is the reason we all got trained on the 300 to freeze the cabin in descent. At least new 800s will make the situation better.
As for it being SOP to turn the APU off.. It is. But if its too hot, we have the authority and backing of the company to deviate, as does every single pilot worldwide regardless of airline. Its called judgement.