Weird cooling system problem

[sc2095]

I helped my friend replace his waterpump on his 93 SC2 yesterday, cause it finally died. We filled the system back up with water and coolant, and then let it run to check for leaks. It was working perfectly. We went for a drive, and noticed that the car started to heat up, and wouldn't cool back down. We took it home, and everything seemed ok, but when the car was cold, he took off the coolant resevior cap, and coolant came running out of it. He filled it back up to the lower level, and then went for a drive again. The same thing happened, only it took longer for the engine to heat up. Any idea why this is happening? The thermostat is opening up because both radiator hoses heat up and he has lots of heat in the car.