It very much sounds like this is your actual problem, not the brake module. The brake module is apparently not malfunctioning, just temporarily overheating because of the unusually high current passing through it, and shutting down to protect itself.
Motors draw current equivalent to the load they are under, even until they overheat/melt. It very much sounds like whats really happening is increased mechanical resistance around the operation of the parking brake (ie your parking brake is clogged with dirt or something), which is forcing the motor/actuator to work much harder, so in turn its drawing far more current, which is in turn making the control module overheat.
You need to find/fix the root cause of the motor drawing such high current and don't operate the motor again even with a test box until you know for sure that the brake mechanism is at least mechanically free to operate properly, otherwise you risk damaging/burning out the motor, wiring, and/or the control module.