The batteries will last quite long if you set the display to EVF Auto only. If you use the LCD, then the camera takes up quite a bit of juice.
Don't have a problem with the heat, but it could possibly be due to my setting to the EVF Auto only as well. I'm not saying that the heat is not there.
A set of 2100 mAh batteries should last you abt 3 hrs shooting on a typical Zoo/JBP walk i.e. walk to one exhibit, snap a few shots, carry on moving without manually switching off the camera. My setting for this is EVF Auto, 1 minute auto-off, press the shutter to turn on the camera again.
Noise-wise, if you want to blow up your pics, you might want to consider using NeatImage to lessen the noise, otherwise printing of 4R should not require noise reduction, not noticeable at all at these sizes.