Without a thermostat you have no chance of maintaining (or even reaching) the correct running temperature, if it is getting hot then you have a bigger problem than a missing thermostat which has been removed to cover up the problem and not cure it.
A thermostat allows the engine to warm up by keeping the coolant in a closed system circulating it around just the jacket & heater, at this stage it is not flowing through the radiator. As soon as the operating temperature of the thermostat has been reached the thermostat opens and allows the (now hot) coolant to flow through the radiator which lowers the temperature to below the operating temperature of the thermostat so it closes again thus allowing the coolant to warm up. This goes on all the time the engine is running and maintains a constant water temperature.
If you have no thermostat fitted then there is every chance that the engine will never get up to the correct operating temperature as it is constantly being cooled (over-cooled in fact) but if it is then you have a fault which needs to be sorted rather than being covered up.
Is the engine actually hot or does the gauge just say it is?
Is the rad the correct size and if it is, is it blocked or the fins damaged?
Is the coolant circulating & pressurising correctly?
As already stated, it might (hopefully) just be that it failed for some reason and the previous owner couldn't be bothered to get a new one (worrying as what else might they have done in the name of "maintenance"?).
Keep an eye on it and perhaps check the gauge accuracy.