I use a 2005 model Peugeot 307 with automatic transmission and a mileage of about 485,000km. 

The automatic transmission is faulty and it doesn't run smoothly and sometimes the information screen in the car displays faulty gearbox when the gearbox fails to change from one gear to another and it begins to run roughly and the engine temperature begins to rise fast and it will overheat if I don't quickly turn off the engine and start it immediately and continue my journey.

In recent times while driving, the engine temperature could sometimes rise up to the normal maximum temperature and sometimes exceed it and begin to overheat but if I stop moving the temperature will gradually drop to a lower temperature which is the normal temperature and it won't overheat no matter how long the engine stays on.

The cooling system is in good condition to the best of my knowledge and I suspect that the faulty transmission is putting too much stress on the engine and causing it to overheat that's why when I stop moving or when I stop accelerating the temperature goes down to the normal level.

So is it possible for a bad transmission to cause the engine of a car to overheat?