On Oct 30, 8:24*am, Jules . Anything with a lot of inertia, like slab
heat, is best left alone
unless the period's very long.

Does that necessarily follow? Anything with a lot of inertia will
cool off much more slowly too. So you don't have nearly as far to
recover when you raise the temp again.

Maybe that part of the question should be rephrased as a time
constant.

Drop the temperature by 10 degrees. There will be a transient period
while the temperature is falling. Then there will be a steady state
period while the lower temperature is maintained. And another
transient period while the upper temperature is reestablished.

Clearly energy use is lower during the first transient period, as in
zero.

Clearly energy use is lower during the steady state period due to the
lower temperature setting.

Not so clearly energy use is higher during the second transient
period, your heat will not cycle until the new steady state is
reached.

If lower steady state is never reached because the setback is for too
short a time, then it seems logical that energy use during transient
periods would average to 50% duty cycle. But this isn't necessarily
true, because the time periods may not be equal. Loss of heat to the
environment is not at the same rate as gain of heat from the furnace.