Sound like a fuel problem. Toyota had a real 'hot hard start' problem back then. The intake valves get very carboned up. Read and do this first.
http://www.toyota-supra.info/forums/...injectors.html
It may fix your problem, and certainly is good for your engine.
You MAY have an electrical component that has a bad spot in it that is effected by a hot underhood soak (parking for a while, then trying to start engine). You will have to test parts and 'catch it' in the act.