Starter / Solenoid Issue for 1999 Z71 5.3L

[ldptex]

I have a 1999 Chevy Z71 4x4 truck with a 5.3L engine. I have an issue that I cannot figure out. On warmer days when I drive long enough for the engine to heat up, when I shut the engine off and try to restart my truck, there is no engagement of the starter or solenoid. If I let the truck set for around twenty minutes the engine will start. I replaced the starter/solenoid and that did not fix the problem. My transmission was rebuilt a couple of years ago and when I replaced the starter I did not realize that there was suppose to be a heat shield over the solenoid. The transmission shop left it off. I installed the heat shield but I still have the same issue. This does not happen in the winter time when temperatures are cooler. Does anyone know what is causing this problem. I can't drive anywhere in the spring, summer, and fall without knowing that I will have to let my truck set for twenty to thirty minutes before I can start it. All other electrical (Lights, radio, horn, etc.) work fine during this time.