2002 Chevy Trailblazer rear heat does not work

I had an '06 Trailblazer with this same issue. Every now and then the heat in the rear would stop for no apparent reason, just like you said the blower worked but the air was cold. I took it to my local GM dealer where one of my friends is a service writer. He had it looked at and found that they rear heater core is in the rear of the vehicle, thus there is a pump that supplies warm coolant to that core. What they found was the electrical connector (because the pump is electric driven) was disconnected(ie. broken). They repaired the connector and the problem was solved. This was under warranty so I don't know the cost to fix, I am sure you can do it yourself. The other thing I noticed is that the heat comes out the lower vents in the rear better than the top. The top never seems to get as warm. Hope this helps

Matt