I have the same problem with my daughters '04 Celica GT. It's been in my shop for 3 months now and I am about ready to take it to the scrap yard! In the last 3 months we have put new radiator, new thermostats, new water pump, and now a new heater core (which was a real P.I.T.A). I even tested both the old thermostat and the new one to see if it was defective and both open at about 185 F. I still have the same problem. It will idle forever with no problems, radiator fans cycle on and off as they should, drive it down the road and will briefly overheat and then cool back down. No hot air from the heater no matter what. I have burped the system per Toyota's instruction, several times, and also tried my own "force feed" method of forcing coolant into the return hoses and heater core. There is no oil getting in the coolant, no coolant in the oil, and not loosing any coolant. I can feel hot coolant on input side of heater core, but it never seems to be exiting the heater core, that hose stays cold. The only part of the system I haven't had apart is the tubing from the heater core to the water pump. This appears to go under the fuel injection and intake, so it looks like I'm going to have to remove all that and see if there is a valve or a blockage of some kind. I guess I'm about to tackle that next, but any help or ideas are welcome!