I remember some bulletin on this era of full size GMs involving a blend air servo being bad, pretty big job to do it though. Dash has to come out.
Is the thermostat hot enough. Check first, but probably a 190 degree.
To only thing is can be are the blend doors, since your heater core has hot water flowing though it.
I have a 1998 Chevy Silverado 1500 5.7L the heater doesn't work at all, just blows cold air. I tried changing the thermostat, flushing the radiator, checking the fuses/relays, the heater core is working (I checked the hoses running in and out of it) and it is circulating like it should be and the blend doors are working fine. The blower motor seems to be working because it blows great but it just blows cold air. Anything else I might be looking over or anything I could try to do to get it working?