Heater nightmare

Hi There. I have a hard time finding a problem on my Mitsubishi galant es 2.4 2005. The heater is working hot for about a minute when I turn the air on and then it's cold after another minute. I have checked the thermostat and it seems to open correctly. I have flushed the heater core with water and CLR to clean any possible debris. The water seems to be flowing to the heater core without restriction. The coolant level is also correct. I have removed the glove box compartment to see if the heater trap switch when I change from cold to hot settings and it also open and close correctly. Yesterday, I have notice if the car is parked and I push the gas pedal to about 2500-3000 rpm it get hot but as soon as I release the gas pedal it's cold again. I am starting to thing maybe the water pump is not pushing sufficient liquid into the heater core. The thermostat have no jiggle valve on it I have a hard time figuring what was the correct position to put it. Can a cheap aftermarket thermostat can cause heater problems? Is it possible that the thermostat without jiggle valve trap air into the system? The upper radiator hose is also kind of soft and when I hit the gas it become very hard. Sorry my English is not very good. Thanks, Peter