Yup, its the heater core. I just replaced this on my fiero. This is what you have to do to replace it. Look under the dash, on the passengers side, with a trouble light or any light for that sake. You will see a black plastic casing things. That part is 2 pieces. You have to take off 3 screws (8 mm socket i think)and then the front of the 2 pieces will come out. Have a bucket ready to catch the coolant. I recomment taking the screws out one by one so that the coolant can drain into the bucket as you go. The coolant will probably leak from the joint of the 2 pieces. OK! So after you have all the coolant drained out go to the front of the car and pop the front deck lid. Undo your window washer tanks and move it. ( i just unbolted it from the car and left all the connections still hooked up) Move that aside and you will see 2 black small rad hoses about 1 to 1-1/2 in diameter. They will come up from the ground and turn into the dash. Loosen the 2 hoses, they are held on by hose clamps. Take them off the metal tubes and make sure that you have them facing up so no coolant leaks anyway. Now that you have the pipes off go back under the dash and you should now see the Heater core, There will be a little metal bracket holding it into place. I just took off the top bolt on the braket (8 mm again) and then moved it out of the way as i pulled out my heater core. Make sure that the bucket is under where you are working so that you can just put the heater core into the bucket when you are done.

A way to check the heater core is to drain it out. Get a 5 Gallon bucket and fill it 3/4 full of water, submerge the heater core into the water all but the 2 metal pipe ends, plug up one pipe with your thumb and then lightly blow compressed air though the other pipe. if there is a hole you will see bubbles, if not then you will feel pressure on your thumb from the air.

hope this helps
rate me if it does

-Phil

If there was no coolant under the front hood only under the dash on the floor mats and such, well the heater core is the only thing under the dash...so yeah...most fingers would point at it.

Here in canada i can get one for about $100

brand new, but yers might be repairable, you never know it might be cheaper

but you are able to do this job in a parking lot trust me, all you need is a pair of pliers, 1/4inch ratchet set, bucket, slotted screwdriver

it is not tough at all

good luck eh, let me know how you make out

-Phil

EDIT JUST TO CLARIFY THINGS

As all are saying, it is the heater core. Make sure you put some towels or papers down on the floor in the passenger side to catch any spills. I used a "T" fitting from an old flush kit on the hoses when I pulled them off, so they wouldn't leak all over the place, while I worked on removing the heater core. After you get the new one in, hook up the lower hose and try to fill the heater core up before you connect the upper hose. This will help so you don't have to burp the cooling system again. Good luck, it shouldn't take you more than an hour. The hardest part will be getting the hoses of the old core.

yeah.. the hardest part about the heater core is getting the old lines off, i had to cut one of mine to get it off.. i think it was the bottom, if you do end up having to do that make sure you have enough hose left over! Other than that its all straight forward, good luck!

Lots of good information has been posted above. One thing to remember...do everything you can to save the heater hoses. They are no longer available from GM, and every aftermarket one I've tried has not fit properly. Also...if your car doesn't have A/C, then you'll be pulling the heater core out from underneath the hood, not out of the passenger compartment. The heater boxes are completely different between an A/C and non A/C car, and the procedure is different. If you have A/C, another tip is to remove the speaker grille and speaker from the passenger side of the dash. This will give you more access to the screw on the top of the heater box. The general consensus is to carefully pry up the grille out of the dash...it's held in place by 4 posts. You have to be extremely careful, as the dash is brittle, and can crack EXTREMELY easily. Lay a piece of cardboard over the dash before trying this, to spread out the pressure from your screwdriver, putty knife, or whatever you use to pry up the grille. I have had success reaching up underneath the dash, and pushing up on the posts from underneath. Again, being able to do it this way depends upon whether or not you have the factory subwoofer or not. The car I replaced the core on didn't have it. If it does, you probably won't be able to reach the posts from underneath the dash. As far as the core itself, I was able to buy one at a local parts store for $35. They even had it in stock...didn't have to order it.