Most likely that's problem, But, sometimes a missing thermostat points to other problems. In areas with high lime/calcium content in the water, these minerals build up in the coils of the radiator when the local water is used in the cooling system. This acts as a restriction in the system much like the thermostat causing too much restriction and resulting in an overheating condition. Removing the thermostat tends to make the cooling system work kind of ok, not quite right, but ok. Open the cap and look in the radiator, if the coils are clean brass/copper/aluminum looking, all is well and you need a thermostat, but if you see a white/Grey chalky looking deposit on the coils then that is probably why the last owner took the thermostat out. If this is what you have, have the radiator cleaned by a radiator shop, they will tell you how best to clean the rest or the cooling system and then only use coolant and filtered water.