This does sound like the heater core is leaking and it may be getting the burnt smell from being too close to electrical items such as the blower motor and/or resistor depending on the car.
Either way, it should be repaired ASAP as the burnt smell is not a good sign and this is an indicator of the overall condition of the cooling system.
The heater box, which is under the dash, needs to be removed to inspect for possible damage to electrics, and to access and remove the core.
If the heater core is leaking it is generally from corrosion eating at it over time.
That is why the entire cooling system; thermostat, hoses and valves come into questions as the entire system has some level of the same corrosion or typical wear. The labor to remove and replace the core is pretty intensive as compared to the labor needed to follow through with a good system flush, inspection and replacement of all components and finally a pressure test to ensure a tight closed system.
Let me know if I can be of any further help.
Sunday, November 21st, 2010 AT 4:50 AM