The humming is most likely the charging section of the converter/charger charging the batteries since you have turned some 12v items such as lights or exhaust-fans. The battery(s) also power controls for furnace, refrigerator, some detectors (not on 9v battery), water-pump, and monitor panel.
The cooling fan for the converter/charger only comes on when needed to cool the unit. If you have a 3-stage charger, the batteries will be charged when needed, and the charger will go into "float-mode" when they are fully charged.
It sounds like yours is most likely working normally. Depending on age and shape of your batteries the time to charge can vary (3 to 24 hours). In cool weather and low load the cooling fan is not needed.
Being used to RV's and converter/chargers, we tune out background noise. Our converter is under our couch and not normally heard until things quiet down at night, or TV is turned off. We might hear the hum or fan if sitting there.
Only problem was when we owned our Hi-Lo trailer. The converter/charger and the furnace were under the couch/bed. Hard to sleep with the noise right under you when you first get the trailer.