No, don't heat it.
I used little bits that I rolled into tiny ropes then coiled around inside the wheel and pressed down to cover the areas to be masked. I checked the fit, then pulled the putty out to add or remove a little bit then tried it again until it was where I wanted it to be.
The reason I placed them in the fridge is because the putty will slump within a few minutes at room temperature. I needed to get my airbrush and paint station set up and I didn't want the putty to slump or move in the time it took to do that.
Yes, I do reuse the putty. I suppose over time the paint contamination will ruin it, but for now it doesn't seem to do any harm.
Here's my putty, you can see the rings I made to mask the wheels. You can get an idea of the "slumping" that I was concerned about.
David G.