A thermostat has no affect on engine operating temp.
That's only true if the engine's natural running temp exceeds that of the Thermostat cracking temperature, in which case, with these cars, there's a serious issue that needs to be resolved.
eg, I know most of my own Minis and Mokes, without a Thermostat will only get to around 50 - 550 on a day of 250 - 280 C ambient air temps.
The function of the Thermostat is to get the engine up to a desired temperature and then regulate it at (or close to) that Temperature.
Normal operating temps for most cars is 95-105 Cel (which is above the typical tstat opening temp of 80-87 C). This is where the engine achieves its best efficiency and thus lowest emissions and lowest fuel consumption. Once tstat is fully open, its the rad & fan performing most removal of engine heat. If the rad/fan cannot keep up with engine heat output, then you overheat/boil over. Typically boil over will happen around 120 Cel (assuming you've got a working pressure cap on the rad and a 50/50 mix of coolant). If the rad/fan can handle all the heat from the engine, it will keep cooling down until either engine start making more heat burden (ie reving up a big hill etc) or temps reach a point that causes tstat to begin closing again. Since mini's with the mechanically driven fan always operating on the rad, this is likely to occur in most circumstances at reasonable ambient temps. With an electric fan that comes on/off at set temps, the tstat is less likely to be open/closing regularly to hold temps above their opening point.
An engine without a tstat or a stuck open one, may take a very long time to reach normal temps, depending on how it is driven and ambient temps etc.