Calling a furnace repair service does not have to be a scary proposition. You do not have to get distraught when your furnace needs to be repaired, particularly as the thermometer drops... and there are young children or elderly living in the home. There's no heat and it's well below freezing. But, it's simply not necessary to worry.
Before attempting to salvage or operate water-damaged HVAC equipment, make safety your first priority. Flood water and heavy electrical equipment like air conditioners are a serious safety hazard. So err on the side of personal safety when performing flood clean-up.