Sounds like it is something electronic that is failing when it gets hot. I had a similar problem on a sports car some years ago. I used the wife's hair drier to heat up electronic components one at a time while the engine was idling in the garage, until it failed. Turned out to be the electronic ignition module in the distributer (petrol engine). I confirmed it by spraying the module with a can of "freeze" spray, and the problem went away. I replaced the module and had no more problems.