First, let's qualify this....what type of charcoal are we talking about? If it's BBQ briquettes, then it's a waste trying, all you'll do is shower yourself with cinders and ash. If it's "lump" charcoal, then yes, I used lump charcoal, that I made myself, for several years.
Unless you have a valid way to measure the temp, a specific number would be useless, however, it will be bright yellows range as far as color. That's another that needs qualifying....the heat could be higher or lower, depending on the material/steel.
Rasps, such as in the pic are notoriously difficult to forge weld, especially is you don't remove the teeth on the mating surfaces. There's also the fact that it's rare to find a rasp these days that isn't case hardened (mild steel with a surface hardening treatment). If you happen to use a case hardened rasp, it likely won't weld, and the end product would be pretty much useless....... but hey.....you could consider it "practice"