I don't think it is the battery. When I first got the laptop I had problems with the battery a few months afterwards, but that has been fixed, and my laptop is pretty much always plugged in.

The temperatures I'm getting are:
HD0: 39C
Temp1: 78C
Temp2: 61C
Core: 56-57-80C (it keeps changing)

I'm guessing that's not too good, and I've got my window wide open (it's freezing!) and I think that's helped so far a little as it hasn't shut down yet today and it has been up and running for 2 hours.