A: I have found that the physics of heat flow in basements is widely misunderstood even by people for whom it is part of their job.
The most basic fact to understand is that heat flows from higher temperature to lower temperature. This is a fundamental as the laws of gravity. You don’t let go of a ball and see it rise. It falls. Always. The same with heat, it always flows from higher temperature to lower temperature, always and without exception. On average (I will deal with the area above the furnace in a moment) the house is at say 70F, the basement at say 60F and the outdoor ground below grade is at 50F. Heat flows from your house to your basement and from your basement to the ground. There is a lot of air circulation in a basement, sometimes deliberately because there are vents in the basement, and sometimes just because of convection currents caused by – you guessed it – that furnace. The heat rising from the furnace (lets say the air above the furnace is at 90F) stirs up the air in the basement causing the air to circulate around the basement and warm up the cold walls and floor of the basement (because they are colder than the warm air pushed up by the furnace). In the area right above the furnace the air, at 90F is indeed warmer than the floor of the house which is at around 70F and so heat does flow from this warm-air column to the floor of the room above the furnace. The further away you go from the area immediately above the furnace, the cooler the ceiling of the basement will get and at some distance, I am guessing about 15’, it will drop to 70F. Further away from the furnace the ceiling will be colder than the air in the basement and the flow of heat will be down from the house to the basement. So the ideal situation would be to insulate the entire ceiling of the basement except for a 15’ radius circle around the furnace. You could easily determine the size of this ring by just measuring the temperature of the ceiling of the basement using an infrared thermometer (such as the one I have, the Black and Decker TLD100 which you can get for about $30 at Amazon) during the time that the furnace is on.
I installed the fiberglass insulation on the ceiling of our basement in exactly this pattern. The ceiling of our basement is not insulated in a strip about 8’ wide and about 20’ long above the furnace. The long axis of this strip aligns with the long axis of the basement, which is where I think the convection currents carry most of the heat. Since, now we have heat pumps, we use the furnace only on about 20 days a year this has very little effect, but I think it is worth doing if you are still using your furnace year round.
However, what I did do that I think has a much bigger effect is to insulate the bottom and sides of the ductwork which run along the ceiling of the basement. I did this with 4″ thick fiberglass. This allows the warmth of the heated air inside the ducts to warm the floors above them while keeping most of their heat for the rooms to which the ductwork carries the heat like the bedrooms on the upper floor in the corners of the house. The heat in the ducts is no longer warming the basement. This is part of the reason the temperature in my basement dropped about 8F and the temperature of the air coming out of the vents in the bedrooms increased 5-10F.
Overall, the trick is not to heat the entire house. It is to heat the parts of the house you live in.