91 Aerostar cooling system

91 Aerostar 3 litre V6 automatic. Problem started sounding like something "thumping" under the hood. When checked, the radiator and heater hoses were expanding and contracting with each thump and could hear the thermostat banging open from the pressure. Did flow tests and pressure tests on system and everything seemed Okay. Pressure left on cooling system all night and pressure held- cylinders didn't seem to have coolant in them.
Pulled the heads and found that one head gasket could have been leaking (small mark) so, both head gaskets replaced, heads looked good.
Engine ran fine for a week then started problem again. What could cause this "cavitation" in the cooling system? It will also thump for about 30 seconds after the engine is shut off.
It seems that compression is being put out into the water jacket somehow, but if something is opening up when the engine gets warms, shouldn't it be a constant pressure into the cooling system (more like a compressor) when the engine is idling? This is more like a popping sound.
Any ideas or help appreciated.
Thanks

It was the water pump- pulling in air. Replaced pump again and everything okay

this is good to know... I'll keep this in mind if I ever encounter the same problem.