I don't think the actual temperature difference matters. Look at it from a conservation of energy viewpoint: the total heat lost from the house to its environment (by conduction and convection) must equal the total heat produced by the heating system, as (effectively) none of it goes anywhere else.

And if you keep your house heated the whole time, the steady state is when the inside surface of your walls is at room temperature all the time. This means that the temperature difference measured across your walls is always as high as possible (for it to be any higher, the inside surface would have to be above room temperature, which never happens).

But the heat flow (heat loss) is proportional to the temperature difference across the wall. So heat flow, under this plan, is always at maximum, 24 hours a day. Which means that any other plan -- even letting the house cool down for only an hour before turning the heat back on -- causes less heat flow into the environment, and thus less heat production by the heating system, and thus lower bills.

The energy needed to reheat the walls, while no doubt a lot, is not as much as the energy needed to keep them permanently warm.

Peter