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My guess would be a stuck temperature actuator. Pretty common failure.

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The actuator is located on top of the HVAC case on the right hand side. You may be able to get to it by removing the glove box,but if you can't you will have to pull the dash back.
Either way not too bad of a job if you are pretty handy.

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Not the best video but it shows where it is clicky

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There is another issue that could be causing the "no heat"

I had the same issue with my 2001 Blazer.  It had the dexcool antifreeze in it that is what is causing this common problem with the S10 family.


It is possible that the heater core is plugged up.
I cleaned out mine this way.
It is a bit messy...
When the engine is cool remove both heater hoses from the engine block/radiator end not the heater core end.
Next take one hose and position it downward into a bucket or pitcher.


Hold the other hose up towards the hood and let the antifreeze in the core drain out. Once it drains pour a pitcher of water thru the core to flush it out some.


Now you hold both hoses upright and pour vinegar into one hose until you see it in the other hose filling the core.


Let the vinegar sit for a few minutes and dump it out into your drain bucket you can do the vinegar flush a couple times if you feel it necessary.


Now what I did was I got several pitchers of HOT water and flushed the core out a couple of times
Reattach the hoses to the engine block radiator and refill the radiator with antifreeze. Run the engine to operating temp and top off the antifreeze(overflow bottle) if needed.


Check the system for leaks and your done.


Worked like a charm and I have not had any other issues with the heat since.




And IMO if it were me and the vehicle still had dexcool I would change it to regular antifreeze.






 

Quoted:
There is another issue that could be causing the "no heat"

I had the same issue with my 2001 Blazer.  It had the dexcool antifreeze in it that is what is causing this common problem with the S10 family.


It is possible that the heater core is plugged up.
I cleaned out mine this way.
It is a bit messy...
When the engine is cool remove both heater hoses from the engine block/radiator end not the heater core end.
Next take one hose and position it downward into a bucket or pitcher.


Hold the other hose up towards the hood and let the antifreeze in the core drain out. Once it drains pour a pitcher of water thru the core to flush it out some.


Now you hold both hoses upright and pour vinegar into one hose until you see it in the other hose filling the core.


Let the vinegar sit for a few minutes and dump it out into your drain bucket you can do the vinegar flush a couple times if you feel it necessary.


Now what I did was I got several pitchers of HOT water and flushed the core out a couple of times
Reattach the hoses to the engine block radiator and refill the radiator with antifreeze. Run the engine to operating temp and top off the antifreeze(overflow bottle) if needed.


Check the system for leaks and your done.


Worked like a charm and I have not had any other issues with the heat since.




And IMO if it were me and the vehicle still had dexcool I would change it to regular antifreeze.






 

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So I put in a 12" piece of clear hose in the line that goes in by the thermostat.  The flow is very weak, as in not enough to keep the clear line full.



I guess the next step is to flush the core.



I do have more heat than before, but as much as it should.

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Could be the blend door actuator gear broke.

http://i16.photobucket.com/albums/b40/JoshB_/wrongpart.jpghttp://i16.photobucket.com/albums/b40/JoshB_/relay2.jpg


Your heater core could also be block so a reverse flow flush might be in order