Hello if welcome to the forum, the truth is that you give few data from your car to see well what the problem is. But if I'm not mistaken, that car was wearing a Bosch Ke Jetronic injection system and the failure can be in the thermore resistance that measures the engine temperature.
I explain, when this probe stops working, the switchboard (which is quite primitive) takes as a reference that the engine is cold, injecting a lot of gasoline. As the engine is heated, you should correct the dosing of the mixture, but since the probe is broken, it continues to inject the same dose.
When the engine is hot, it simply drowns and ends up and until it cools, it does not start for being "drunk" of gasoline.
To check it you just have to take out a spark plug when the engine has stopped hot, if it is covered with soot it is because there is too much gasoline in the mixture.
Greetings and if you publish another post detailing a little more type of engine, type of injection, if you pull, if it smells a lot of gasoline ...