I wouldn’t go for any 300 mile weekend trips but the engine isn’t going to self destruct from what you are describing.
be sure to check your oil levels and your coolant levels. The smaller tank with the pressure cap should always be filled and the longer tank, the overflow tank, should not have a pressure cap and generally finds its equilibrium somewhere around 1/3 to 1/2 full.
in the past when I have removed the thermostat I will refill coolant at that point before reinstalling the thermostat. there might be some advantage to raising the front end of the car, to keep air from getting trapped in the back of the Heads, if you try that approach
make sure the bleeder at the top of your radiator is open
Larry