Hi, not sure if you guys have checked this but the mysterious cutting out could be that pesky rod that pushes the fuel pump. As the crankcase heats up the problem gets worse as now the rod is even shorter. It cools a bit then starts pumping again.
It runs strait off the cam and wears with time, could explain overheating too as the poor thing would be gasping for fuel, a it like Pete when he arrives at Retro rides looking for a beer. Might have missed that if you mentioned it.
I've pulled my manual pump off, installed a pressure regulator and running an electric pump, Installed an extra breather where the old pump was better breathing and more constant fuels pressure on the needle and seat is the theory.
It's just a thought.
You do know what Fiat means don't you? Fix It Again Tomorrow

But seriously when you get them running well they can be very reliable and cover some impressive distances.
In my experience there are two major reasons for overheating, Ignition timing or running lean.
It may sound very simple but you have to simplify it or it turns into a witch hunt. Thermostat in my opinion is extra weight on the air cooled and BIS.
Oil coolers help imensly if you start pushing for higher performance and the old boot lid opener on the air cooled helps hugely too. I know oil etc is a factor but then if it overheats it destroys the oil.
I had an electronic ignition thing that had curves you set with toggle switches. It now lives in a box in the shed, I think the guy who made it must have had a bad day or something because no matter what I did with it the car overheated. The simple one that goes where your points were is my preference.
Not sure if that rambling is of any use, good luck with that one
