What happens if a F1 car overheats?

It usually catches on fire as seen at Monaco with one of the Marussia's. It can happen when the car is stationary for too long as they have no fans. Only air cooled radiators.

The engineers can see the data so they may ask to save the engine before it damages itself but it really depends how quickly it does overheat.

When the car overheats, damage can be done to fuel lines, exhaust systems and even the pistons.