I have a different opinion about your situation. If you are breaking in a cam then of course you need to run it for a certain length of time. The best way to make sure it stays cool would be to run it without the thermostat and work on that later. Also it is difficult to fill the system without leaving some air when the thermostat is in place. Without it you should be able to avoid air. One thing that I do is remove the heater hose that connects just below the thermostat. I then fill the rad until it runs out there, and then replace the hose. If the rad is filled up to the top the expansion will cause coolant to come out when it warms up.
