Probably not much help, but I have the same problem with my Jaguar, when it runs enough to get the engine hot, then is parked in the heat it will not restart until it cools way down, and just like you everything happens correctly but the engine just fails to even try to turn over. The first time, I thought it was a weak battery, but it turns over and starts right up every time when it can be cooled. I have resorted to placing a fan under it when I pull into my garage, outside the workaround is to open the hood.
Have been successful enough with the workaround I have not tried to troubleshoot. It must either be something shorted or open circuited in the heat, or else something dependent on engine temperature, such as the aux fan control circuit. Good luck, and if you stumble onto anything, let us know!