In the end, the engine temperature depends on the capacity of the cooling system. At one extreme, put a 190 degree thermostat in an engine, and use a radiator from a Honda CX500 motorcycle. It won't take it long to get really hot, and it won't stay anywhere near 190 degrees.
On the other extreme, add on a radiator from one of those big emergency generators. It will take the normal amount of time for the engine to get up to 190 degrees, before the thermostat opens, but you won't be able to get the temperature to go much higher than that no matter what you do.
There are factors other than the radiator involved, but I would suggest that radiator cooling capacity is THE big factor in engine temp.
The same is true of oil coolers. A 350 with a radiator from a Honda CX500 can be kept below 200 degrees if you have a big enough oil cooler. Both systems do the same thing. The only difference is the cooling medium, oil versus anti-freeze/water mix.
The oil's primary function is not cooling, though, and it isn't as good at cooling as water/anti-freeze, but it does work.
