Without a thermostat the pump will always keep the coolant circulating. Depending on the volume of coolant the engine may never warm up or it may overheat quickly. The job of the thermostat is to control the flow so the proper volume if coolant spends enough time in the radiator core and cool enough to maintain the engine temp at or near the thermostat rating. In some of my old Ford flatheads I removed the thermostats in the summer and it only overheated when stalled in traffic. I put them back in the winter because it would not get up to a warm enough temp to run well or work the heater. This worked for me but it was not right. If This was mine I just drive it until boiling over became an issue. I would note what temp the gauge shows in different situations and learn how it works. On my '53 Chevy pickup the gauge shows a little less than 180 when normal above 185 it is boiling. It has been this way for 20 years. It rarely boils.
