Can Incorrect Timing Cause Overheating

Late or retarded timing can cause overheating as the compressed air/fuel mixture is still burning very hot when the exhaust valve opens. This creates too much heat in the exhaust port and exhaust valve. This extra heat is also absorbed by the cooling system.

Does timing affect engine temperature?

Advancing ignition timing increases engine temperatures. As you increase towards MBT you get more power but temperatures may get so high that you melt a through the combustion temperature + compression increasing temperatures.

Does retarding timing make an engine run cooler?

Retarded timing makes for a hotter running engine. The fuel is burned less efficiently requiring more fuel for similar power levels. However this fuel IS burning and creating heat as it exits the engine.