Engine components like pistons are designed to be operating at a particular temperature... If you run too cold then pistons don't expand to the right size and shape, you accelerate wear. Your oil doesn't get hot enough to boil off contaminants. The choke on the carburettor doesn't open properly, you burn more fuel, which leads to more oil contamination. Without the thermostat, the block and heads heat unevenly, leading to the possibility of head gasket failure. Also, depending on the design of the thermostat housing, some engines depend on the thermostat to direct water flow. Without it, some areas of the engine may actually be getting too hot.
Running without the thermostat is a bad idea.
Chris........