The engine will not start when hot?

1987 Pontiac Bonneville 3.8 L, V-6 type 1 DIS / non turbo: Cold starts every time, idle sometimes lopes and/or erratic, but performance is beautiful, good power, good pick up, will run all day long, no over heating. Fuel efficiency good, but turn engine off and a complete no spark situation to all cylinders if I try to restart. Once the car sits for a period it starts right back up and performs as stated above. Most obvious conclusion, thermal problem. Which part of the (Brick), top (Coils) or bottom (Module) has been most commonly diagnosed for this problem, in the vehicle described above? Remember, I am not asking what's causing the problem with my car, but to the best of your knowledge, what has been the most common diagnosis and repair of this problem, with vehicle described above? One connection where wire from module plugs into coil pack, connection was green and corroded, cleaned, it helped, but didn't cure. Coil module, affectionately known as "the brick." Its top section contains three ignition coils, each with two the bottom section of the coil module contains the electronic circuitry, neatly potted in bulletproof epoxy.