Do you have central air? If so did you notice the same smell, if yes then I would get all the ducts cleaned and check for mold in the area/room that your furnace is in.
If no I would have a technician or heating company come out and service your furnace. Good to do every few years anyway. Mention to them the issue they may be able to figure it out for you.
Do you get water in your basement, or is it damp? Then you could be smelling mold. We had a horrible, horrible issue with a damp then wet basement which leads to mold and mildew. Since the furnace was in the wet/damp basement in moldy conditions it was pulling that moldy air through the furnace and I was starting to get really sick and to me the smell was bad. My husband only noticed it when it was really bad. In this case get someone professional mold cleaners to clean the moldy area well and clean the furnace and ducts. Sadly for us it took waterproofing the basement to fix our problem and smell, hope you do not need to go that far.