Roomates car did the exact same thing. It would cut off once it got warmed up and then wouldnt start until it cooled all the way back down. His ECU ended up being the issue. I would try and swap if you can get a hold of one to try
98 Eclipse GS TurboBuilt motor - MS2 - Holset hy35 - Zoom Stg 4 Clutch - 57.5mm TB - ARP Headstuds - Turbonetics wastegate - 3" Turbo back - FMIC - Greddy RZ BOV - Walbro 255 - 650cc Injectors - Fidanza Flywheel - Cobra calipers w/ 13" Rotors - Oil Cooler - DevilsOwn meth injection1981 Chevy Scottsdale1987 Nissan 300zx - Chump Car2001 BMW 325i