If the steroids placed in the epidural space are particulate, then can't they melt once in the body and esp. under heated conditions like exercise or fever?

Unlikely happened: In unlikely event of particulate steroids in your epidural space, ask your doctor how it could happen. These particals will get absorbed or will be encapsulated. Your question leads to other concerns. Talk to you physicians.

They don't melt: Sounds like you are referring to an epidural injection with a suspension (e.g. Depo-medrol) vs. A aqueous preparation. The particles in the "depo" form dissolve very slowly thereby providing a slow local release of medication. They don't "melt" due to heat.