I would not run a car without a t stat. The heat needs to be there to evaporate any water you might have from condensation. The
oil cooler was on the original cars because racing was presumed to be a possibility. My car does not have an
oil cooler but it does hold a lot of
oil, which keeps the temp down.
A Mercedes gullwing comes with dry sump and holds about 14 quarts. One guy who rebuilt a lot of them said he typically runs about half that much oil to allow it to warm up. He says he has a tough time getting people to run their Gullwings low on oil though.