Turning off 'push', or checking that the APN settings are correct, certainly seems to be the logical fix for this. I urge anyone who is having problems with the battery life to run the phone connected to your computer whilst the iPhone Config Utility is running, that way you can see the error for yourself - if it isn't the same one I described, post it here and I'll try and provide a suggestion as to how to fix it...
But remember, your phone is basically a small computer - the battery is draining really fast because the CPU is doing an awful lot of work, same reason for the heat...
MJ