Follow the cable. It should open a door for the heat to enter the air flow. It's close to the HVAC unit.

Just pull the cover off. The cable end probably fell off the temperature knob.

 

Pull the center knob and remove that screw. Pull that black panel off and look to the far right for the cable. Like @75aces mentioned, it probably just came off when someone else was messing around back there. My other (far left) knob: the cable was still connected but came out of the clip that held the cable in place. just fixed it recently

 

Update - have heat now. For anybody who reads this - in the 1st gen Matrix this cable does NOT go under the hood.

There is a white plastic slider under the glove box - huge, a few inches, with blue cable pulling it in sem-circular movement. It is under the left end of glove box, not behind the box. I moved slider forward - now heat is blowing.

Bad news - the cable is cut off the pin on the slider. Apparently the previous owner couldn't move the knob when cable got sticky - happens with time. He tried so hard that cable got dislodged from pin on the knob (I found this out by feeling behind the panel without removing the panel). Instead of removing cable from the slider he cut it off, to move slider by hand. I doubt that with a few inches of cable missing I can make it work. Besides, I tried to pull it, it doesn't move inside the sleeve.

Now, where do I buy this cable or what is the part number? I've lost confidence in the shop to get it.

 

Junkyard. Practice pulling yours first so when you go, you already know the process.

 

I heard this cable is getting sticky with time and it can't be helped, Teflon sleeve wears out. Junk yard cable could be short-lived. Matrix is "almost" Corolla, one would think there are tons of this in stores, but - nope...

 

Might be part of the HVAC system. Try toyodiy.

 

It is indeed part of HVAC. Found it at the parts dealer, $12 CAD part, $20 shipping - oh well, this is Canada.
Toyodiy is an interesting resource, thanks. They don't have a Matrix but many things on Corolla are similar.