Last week I flew ATL-MSP and noticed the cabin of my 757 was warm on boarding, and it only got worse. APU was inop. It took ~10 minutes to get one engine running, but they wouldn't throttle it up until we pushed back, which meant that we were sealed in an uncomfortably warm cabin for an extended period of time. It got pretty warm in the cabin, and this was in the morning on an overcast day.

Jetway conditioned air doesn't work very well for bigger planes if their APU is inop.