The cooling system is designed to be able to keep the engine temperature within an optimal operating range regardless of temperature and conditions. In other words, the system is designed large enough for "worse case" operation. In that "worse case" situation, the thermostat would be fully open.
The thermostat works from both ends to keep the engine temperature within operating range.
On the cold side, the thermostat keeps the coolant inside the engine when engine temp is below the optimum operating range so that the engine temperature quickly rises to within its optimum range.
On the hot side, the thermostat regulates the amount of coolant to the radiator so that as much heat as is required is released to the outside air to keep the engine from overheating, but not so much that the engine temp drops below the desired operating range.
If you don't have a thermostat, and assuming the the cooling system is working properly and sized properly, the engine will nearly always operate at well below its optimal range, unless its under heavy load on a hot day. Having an engine too cold is almost as bad as an engine too hot.
Think of the furnace in your house (use A/C if you live in a warm area). Its big enough to keep the house at say 68 degrees, during the worst cold snap you'd expect in your area, which might be 10 below zero. If you run that furnace continuously when its 60 degrees outside, your house is going to be well above 68 in short order.
On the other hand, when its 40 degrees and you turn on the furnace for the first time, you want it to run continuously up until the house is at 68, then you want the heat regulated so it doesn't go over that.
The thermostat in your house does the same thing that the thermostat in your car's cooling system.