Over heating and intermittent heat

Over heating and intermittent heat. I have a 2004 matrix, about a week ago the car began to overheat. I took it to my shop and they said they thought it was the thermostat and replaced it. It will run for awhile and overheat (blow it out the overflow). Back it went, they checked it for an airlock and head gasket ( with a dye test), no head gasket problem, and the system was bleed twice. Was great for a day and overheated, oh by the way the rad cap was changed as well. The water pump was changed 2 years ago and the shop says it may be the pump sucking in air through the shaft, as it seems to circulate. Is there any type of bypass valve that could cause this type of airlock, I and the shop are at a loss. I am thinking of pulling the pump and see if the fins and seals are fine. Thanks for the help. Tom M