straightening a bend tempered axle

I'm sure you'll get more informed advice from others. This is outside my field of expertise and personal experience. What I've heard or read about the situation you describe leads me to believe that you couldn't use your hydraulic press slowly enough to safely straighten the axle with it. The rate for straightening tempered steel would be more like you would get with a 20oz ball peen hammer, never striking the metal hard enough to actually see movement.

I'd guess that you wouldn't use heat with this method, but that's all it is---a guess. I know that light peening is useful in relieving heat induced stress in weldments in some unforgiving metals, like cast iron. That's why I think it might be appropriate for tempered metal. I also remember reading about a machinist who took deflection out of a shaft in a large piece of industrial machinery by tapping it for eight or ten hours. He saved the company some huge amount in repair costs, and a lot more in avoiding lost production time. I believe that his supervisor told him that the company was so grateful that they had decided not to write him up for working overtime without prior management approval. (I made that part up, I don't know anything about the circumstances.)

Good luck, Stan

Do you REALLY want to mess with a BENT axle?