As @jrd51 described, it is easy for a scion to get ahead of itself and die back before it can callus enough to survive. But sometimes, if there is a second or third bud on the scion that hasn’t pushed, it may still have a chance.
For most grafting, I’m happy to graft with a single bud on a piece of scion, but for persimmons I often do 2 or even 3 buds in case this happens. I grafted a few small trees with some very thin scion that may have been cut close to when the tree was waking up. After grafting, the temps didn’t warm up as I had expected and the little trees didn’t callus enough before pushing the first bud. But after that first bud pushed and then dried up and died we got enough warm weather and there was enough life left in the remaining bud that hadn’t pushed yet that 2 weeks after the first buds died, the second one is waking up and hopefully this time the trees have enough callus to sustain them. In this picture you can see the dried up growth on the left and if you look closely the top bud is now pushing.
This one (out of focus) you can see is further along.
So if you have remaining buds on a scion that has died back it may still make it.
For the heat source, here’s a rather long thread that covers creating a hot callus pipe: Hot Callus Pipe DIY