prostart remote start issues when engine warm

hey out there

I had a prostart CT-3471 TW installed in my 97 chevie 4x4 1/2 ton truck. Everything seems fine when the engine is cold. When the engine is warm however, the engine barely turns over and I have to wait for the engine to cool down alittle bit before it will start. Obviously this causes me abit of angst.
Battery and Starter motor are approximately 5 years old. Tested Battery has 12.41v prior to starting, drops to 10.50v when engine turns over. Haven't done a volt test yet when the engine is warm.
Could it be a weak battery???? Cleaned the battery connections which helped alittle bit. Truck used to start just fine before the remote start was installed.
Had problems with starting the truck five years ago when engine was warm anda replacement starter motor fixed that problem then.

thoughts advice????

if is possible that the starter motor gets weak when hot. this would occur with a very old starter motor or a rebuilt starter motor after a few years. your 1997 if used in bad snowy weather often this would also include the fuseable links and wires going to the starter from battery. also the solenoid nut feed connection to the starter motor. all connections must be checked and also grounds for security/corrosion.