You sure its from the rear end? I suppose it could be the bushes on the suspension. Not sure why the engine being hot would make a difference. Under load makes sense.
If the engine is heating up more when under load, it means that there is something in the cooling system not quite working as it should. What engine do you have?
Mine gives a squeak when the aircon is on. Doesn't happen constantly, but whenever the compressor kicks in, squeals a bit and then settles down. Turn the aircon off, stops.
Other things on the belts are:
alternator - unlikely
power steering - seems unlikely.
I guess could also be the fan? It's got a hydraulic clutch that kicks in when it heats up. It sits on the outside of the water pump. If it's putting extra pressure on the water pump which is causing the squeak, you'll want to get on to that. It also matches with engine getting warmer, perhaps?