1992 Mazda MPV Weak Heater

I can't seem to get good heat out of my heater. I had a mechanic flush the core but it still doesn't work. Also, there is an passenger heater that doesn't seem to work either. The engine seems to be running at the correct temperature and I recently had the radiator replaced (the heat didn't work before either). If you turn the fan off for a few minutes, than put it back on, it blow reasonably hot air for a few seconds, then it cools back down. I am guessing that the heater core is partially blocked, but I was just hoping that there was another possibility since it is a big job to replace it.