Q: Overheating issue

All started with a burst hose. Noticed my temperature gauge was buried in the H, so I pulled over, towed home, And replaced the hose. now I have an air leak, somewhere. The car concistantly overheats a few weeks after I top up the coolant, and burp the system. I open up the rad cap to see that my coolant level is way down. I am not able to locate the leak. No puddles form under the car, I used a block tester to test for hydrocarbons, new rad cap, new thermostat, new hoses, new radiator, (from other issue) and nothing. Pressure testing resulted in a definitive air Leak. But something new happend the other day, I was overheating while idling, and i pressed on the gas. My temp gauge went down when I did so. The rad fan always comes on no problem, new fan switch, new relay. Very strange. Checked out the timing belt to see when the last time it had been done was, looked pretty new. It may be foolish to assume that because the belt is new, the water pump is too. No milky oil, and atf is fine

My car has 310000 miles.
My car has an automatic transmission.