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Dust accumulates on the furnace heat exchanger and burns off the first time the furnace fires in the fall, that is a common problem. That generally only happens once a year however.
Let me know if that rings any bells on your end or not, we can go from there without any time limit,
If you do not get the smell in the rest of the house, it is possible that a bad wire connection is over heating in the wall, at one of the junction boxes, It is unlikely however that would be occurring intermittently though, however if it IS actually occurring, it is a *dangerous condition,
There is a high probability that is an electrical issue, You should unplug all of the appliances in the rooms and turn off the lights, it the smell abates you are relatively safe, if the smell does not abate it could very easily be a dangerous electrical short condition
In that case, turn on the lights in the rooms, and plug in a vacuum cleaner or lamp, then go to the house main breaker box and turn off breakers until you loose power to the rooms in question, and leave that breaker or breakers OFF,
If the smell abates you are most likely very safe, if not, it IS an emergency,
In that case you might want to turn off the main breaker at the top of the house breaker panel.
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Be sure to stay in touch after rating my advice if still smell anything, we need to stay right on top of this.