I mentioned cooling with both air and oil previously. Obviously if there *was* any electrical issue it has been sorted, since the engine starts and runs OK. The GEN light coming on sounds like a red herring, because as the engine starts to stall the revs drop and the light would come on anyway.
There are two questions, it seems to me: why does one side get hotter than the other, and why does getting hot stop the engine?
If an engine gets too hot, it doesn't just stop only to be startable again when it's cooled, it keeps running getting hotter and hotter until it seizes. So there are in my view TWO problems - one is that one side is getting too hot (so check blocked cooling airways, and blocked oilways - sorry, but an engine strip might be in order); the other is that something is breaking down when it is getting too hot (so this might well be an electrical item such as the coil - however, this issue can be 'solved' by not letting the engine get too hot in the first place. So that brings us back to a blocked airway or a blocked oil way.
There is one other way of looking at this: not enough cooling in one side might also be caused not by a blockage on *that* side, but by a massive leak on the *other* side.
For both oil and air, the cooling fluid comes from a common source (pump and fan respectively). It is then split into two halves, one to each cylinder. If one of those halves has a huge leak in it, allowing the fluid to escape, the *other* side will not get its full share of the fluid, and hence not get its full share of the cooling.