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I have a hunch it is loose solder joints on 2 resistors that are on a circuit board.
* Note: caption is misleading, resistors were not burned out, just the solder was loose
That's the "good news".
The "bad" news is, it is located on the interior side firewall, behind the brake pedal, next to the steering column and will require you to contort your body into awkward positions to reach.
You'll have to remove the hush panel, and look for a black plastic box.
It has one crazy nut holding it IIRC(it's been years since I did the same fix on mine).
before you REALLY get involved with this, check the plastic clip on the blend door which connects the actuator motor with a rod that connects to the blend door......if that is broken or stripped out, you will have the conditions you describe (and in reverse also!).....
Thank you will check these ideas...the blend door connection is it on the firewall side of heater?
look up INSIDE of the passenger floor-board area after removing the "hush' panel...you'll see a small motor attached to the heater box...on that motor you'll see a rod attached with a clip to the motor... on the other side of that rod that you can see ONLY after removing the heater resistor from the heater box in the engine compartment, you'll see another clip that attaches the rod to the "blend" door....if either clip is stripped or broken, it will and can cause the problem you are having.....*also, just to sure, disconnect the battery for a few minutes to see what (if any) effect this will have)...
..i figured that someone would post these sooner or later since i misplaced my copies........also, the clips are no longer manufactured by gm...i found a source for the clips but, have to "re-find" that info......may not even be relevant here yet....
Thank you guys and for the pictures (89 Paul in Cal) looked in the heater hole by the firewall and the blend door would move freely so knew something was not hooked on, it is the clip under the dash on the motor the little clip is broken so will have to find a new one or something that works, little hard do get to when you are upside down and legs over the seat, than try to get out... Pays to have friends that have worked on these before.
Just a follow up..Got a clip today not the exact one but got it to work, took afew hours, trying different tools until it snaped into place put it back together and now, I HAVE HEAT.
Thanks Again