I just read that if you are in RUN and the engine is NOT running, you are draining the battery through the alternator. The regulator is supposed to maintain a certain voltage coming from a running alternator. Have you tested the alternator? Running, it should be around 14 volts. As for hot stalling, a few common issues are possible. If the heat riser valve on the pass side exhaust manifold is stuck closed, all the exhaust from that side is forced to pass through the intake manifold, under the carburetor, and that will actually boil the fuel, causing a stall. If you are running a GM HEI, the module is susceptible to heat causing it to fail until it cools down. That is why they use some heat sink grease under the module to dissipate the heat. Back when HEI was new, GM suffered a lot of warranty problems until they figured out the grease thing. A poorly situated external coil can get hot, shut down, and seem fine once it cools off. This is about a running hot stall. A heat soak non-start is different. A hot car is shut off, the starter gets over-heated from the exhaust pipe or headers, and won't start, or labors to start. Once it cools off, it starts up fine.