I had this happen on a car of mine. For me, it was a clogged heater core. The core will warm up a little if the fan isn't on, but then just gets stone cold after running the fan for a few seconds. And while driving, it's always pushing some air through the vents, so the core won't heat at all while driving.
It's a sign that you should have the whole coolant system back flushed. At the very least, the heater core needs to be back flushed. There are some great demos on you tube that show even using cleaning chemicals. When I did mine, I just used a garden hose hooked to a hot water line in the house. Worked like a champ and the heat is so freaking hot now.

 

Has the thermostat been replaced?

 

I have not replaced the thermostat. It starts out in the cold range and then rises into the mid range where it always has ran.

 

If a clog is what it turns out to be, here are two really good videos about unclogging a heater core. The first talks more about methods and chemicals, and the second is a practical demo.

http://www.youtube.com/watch?v=mMp82zLVxoU
http://www.youtube.com/watch?v=dcL_0TWeZJY

 

I had a GMC truck that did the same thing and a new thermostat solved the problem. Temp gauge in cab read the same as it always had.

 

Better yet, try this thread

http://www.dieseltruckresource.com/d...d-t210483.html

 

Bringing back an old thread as I suffer the exact same problem.
Did the flushing of the heater core do the trick?
Im going to do the CLR flush at the end of the week here at the shop as I suffer the exact symptoms.