It's good to think about heat, but don't be paranoid.
You won't affect temper if you stay below temperatures where you could sear a steak.
You can use a dremel wheel no problem, and a belt grinder as well. No need to spray water over the belt. Just grind and dip.
Btw, I never put the edge on a a tool rest.
Just hold the spine and manipulate the razor over the belt, letting the belt run spine to edge.
If you hold it horizontal, you might risk breaking off a piece of edge.