You may need to clean your heater. It may just be dirty. We had the same problem a few years back. Turns out, a mouse made a lair in the heater and all the stuff it gathered started to "burn" when we turned the heater on (this is also possible, although it sounds ridiculous ).
The blower motor could be starting to fail, when the insulation inside the motor burns, it gives off a terrible odor. Check that first, as you didn't state how old your car was. Or have a repair shop look at it for you.
Previous answer is good answer. Also might have a plastic bag that was sucked up when the ac was on. Good news is that it won't catch on fire, but does need to be cleaned out. If you have a cabin air filter, take that out and then you will have some access to you blower area.