richer AFR and cooling down

How can find out combustion chamber is too hot and need richer AFR to make it cooler ?

up to now in lessons you talked about cooling effect of richer AFR but I can not figure out how we can understand it need more fuel to cool down the cylinder ?

In practical terms, we first use rule of thumb for how rich the engine should be during heavy loads. So for example, about 12.5:1 on pure gasoline (no ethanol) is a good range on a lot of non turbo gasoline engines. On a boosted engine you might be around 11.0:1 . Then you might look at a temperature gauge to see if the exhaust is getting too hot. Typically limits are between 900 and 1000C, but it depends on the application and where you are measuring. At that point you advance spark or make the mixture richer.