You should use a thermostat. The F & 2F thermostat just doesn’t simply open and close like some other vehicles. It also controls the bypass function of the cooling system. When the engine is cold the thermostat is closed to the engine but also open to the bypass, so the water just re-circulates without going through the engine. Hence, a quicker engine warm up. When the engine warms and calls for cooling, the thermostat opens and closes off the bypass.
With the thermostat missing, the bypass is always open, and you’ll never get all the water circulating through the engine because a portion of it will bypass through the open port. The bypass is the small short hose that goes from the thermostat housing to the water pump.
When you get a thermostat, and you should, put it in a pot of water on the stove to make it open and observe the function. It’ll all come clear. And when you install it, you’ll need two gaskets. One between the two halves of the housing. And then the ring gasket that goes on top of the thermostat.
Feel lucky that you got the t-stat housing apart. Steel bolts in the aluminum housing are prone to seize up and often strip for snap off. Anti- seize compound or grease is recommended.