Heater cores are never fun.
Never had to do one on a GP yet, but never had much fun on my 87 or 94 Cavaliers I used to own.
I know they are tucked up, well inside the dash, behind the radio high if that gives you an idea. Here is an exploded video of mu dash when I was tracking down an electrical issue, maybe it might help some.
But if you think its clogged...might test that by disconnecting the lines that come from the fire wall, and connect under your alternator, into the aluminum bracket the alternator is bolted two. Undo BOTH lines, and let one hang down. Get you a garden hose, and make a seal between the hose and the rubber line to the heater core with your hand, and tun on the water. If it flows out, add more water pressure till thats maxed out, and its flowing out the other hose quite well. I would do this till the water if perfectly clean, and you don't see or stop seeing chunks of stuff coming out.
So thats clean...and the heats not putting out.
Then you might look to your blower motor inside the car, on the passengers side as a problem...OR as many have seen and I believe has already been suggested, look into the blower motor resistor as a problem too.
I replaced the GFs blower motor as hers finally died on her this winter, and now, her fan's OFF position is the #3 fan setting. So #4 is low, and #5 is high and thats it. I have a new resistor to install in it, so she can get her #1,2, and 3 back...but getting the time to do it...ya...working on that.
Hope that helps some.
I flushed out my car after my sisters system clogged up on her Regal.
I run the green stuff, and life worry free.
~F~