1973 911T won't start when hot

What is your question?

Every time my car gets hotter than about 200F and I turn it off it won't start. I believe it is an electrical problem as it is just dead. Sometimes it will start and run for a few seconds and will then just cut out immediately. No splutter or rough running just dead stop. I wait for it to cool and it starts immediately! It has an immobilizer and it seems it could be this causing the problem but it spins over well. Also the charge light comes on and stays on even when the motor runs when this is happening. I am wondering if there could be any overheating auto cutout or anything else of that nature? Any help would be greatly appreciated