Perhaps making the razor hot might allow it to be more easily straightened when the blade is put in a vise.

I doubt that it would do so in a meaningful way. If you google “yield strength vs temperature carbon steel” diagrams (or “reduction factor”, or “tensile strength” they would be related) you’ll see that regardless of steel type, not much changes between room temperature and, say, 300ºC and that’s getting close to tempering territory. It makes sense that softening the steel happens at temperatures at which we lose the harder forged steel microstructures (=losing the temper)

I’ve had zero luck. The amount of pressure to get the steel to retake its shape normally breaks the steel.

😬 Yeah, that’s the risk