1999 Chrysler 300 engine problems

If oil is getting into the coolant or vise versa then there is major engine damage whether a crack in the cylinder head or engine block. The damaged head gasket will also cause the two fluids to mix depending on where the damage is. The only way of finding the damage is disassembly of the engine. There is a history of cooling system issues causing overheating resulting in blown head gaskets. So there maybe more issues that will need to be corrected after the head gasket is repaired assuming that is the cause of the fluids mixing.

Their are several things that can cause the engine to overheat. I will list parts or causes of overheating. Water pump, thermostat, radiator, blown head gasket and coolant leak.
Water pump that is no longer pump will cause overheating.
Thermostat stuck closed will cause over heating
Radiator that is restricted or plugged will cause overheating
Combustion gases entering the cooling system (blown head gasket) will cause overheating accompanied with coolant leaking out of reservoir.
Any coolant leak allowing enough coolant to leak out will cause air to enter the cooling system raising the chance of overheating because of the air.

To answer your question. Yes, if there is no coolant circulation then the engine can not cool down. Because these cylinder heads are made from aluminum they tend to warp easiler than cast iron compromising the cylinder head gasket.

No problem thanks for the question.