No. of Recommendations: 5
Heat goes to cold. The greater the temperature difference, the faster the heat transfer.

So the parts of the house you keep warm will always be loosing heat to adjacent areas that are colder. Some will be air moving from one area to another any way it can, that is circulation. Much will be moving "through" walls, floors, ceilings, by conduction. How fast it moves through conduction depends on things like insulation.

Lets assume it is winter. Your basement, where the furnace and hot water heater are, stays around 60. The first floor living area, where the thermostats and main heating devices (output ducts, radiators, whatever) are located stays around what the thermostats are set to, lets say 70. The attic above the main floor has (should have) good ventilation so that is 40.

Heat will travel from the first floor to the basement through conduction. There won't be much loss through air circulation because hot air rises (because it is less dense*).

Heat will travel from the heated first floor to the attic both through air leaks (hot air rises, plus doors, windows, recessed lights, even electrical outlets) AND conduction (floors, walls, ceilings, and especially windows_. It is the warmest part of the house so all heat flow is away from that space.

Heat will be lost from the attic to the out of doors because an attic is supposed to be well ventilated to the out of doors. Which is why we insulate attic floors.

To (finally) get to your actual question, the heat lost from the leaking duct, lost to the basement rather than heating the first floor, partly heats the ceiling and floor near the leak but probably gives up most of the heat to the basement. A basement that might be a wee bit warmer as a result, meaning that "lost" heat will be conducted down through the floor. But all it will accomplish in be basement is an infinitesimal increase in the temperature down there. That will in return slow down the heat transfer from the first floor to the basement but the same soft of infinitesimal degree.

Or, restated more simply...

The whole idea is to heat the living space of the home, and a leaking duct that lets that heat be diverted elsewhere is not accomplishing that purpose. Heating other parts of the house is a waste of money (assuming no issues with freezing pipes or other damage from the cold).

*(Heat doesn't care about up and down, so "heat rises" is poor wording at best. Hot air rises, displacing cold air that "falls", because hot air is less dense than cold air. Which is why a room will be warmer at top than the bottom.)
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