I would say it has more to do with his judgment than anything else. Sorry, but I'm siding with the PAX on this one.

As many have commented, the captain could have refused to take the airplane. Sure, the APU is deferable, but this is where judgment and thinking outside the box come in. In extreme weather, whether it be hot or cold, this borders on a safety issue as well as a comfort issue.

There is one option that I would have exercised: I would have run an engine on the ground until it flamed out from fuel starvation. Now the aircraft has to be towed to the gate.