Edit: as another poster mentioned, for heat pumps (like AC, but frequently not furnaces), it is also much more efficient to run them when it is cool outside (the morning), and then maintain that temperature through the day as a cold reservoir, than to try to expel the heat when it is hot outside. Which is probably a better explanation for the effect.
The rate of heat flow across an insulator is proportional to the temperature difference across the insulator, if I recall correctly.
Suppose you want the inside of you house to be at temperature Tin when occupied and the temperature outside is Tout.
The rate of heat flow across the boundary between inside and outside will be k|Tin-Tout|.
Imagine two identical houses.
In house #1 we keep it at a constant Tin. In house #2 we keep it at Tin while occupied but when empty we let it move toward Tout, turning on heating or cooling when it is going to be occupied again to get it back to Tin when the people return.
For each house, if we plot |Tin-Tout| over time, the total energy used over a given interval will be proportional to the area under that |Tin-Tout| curve.
For house #1, that curve is simply a horizontal straight line.
For house #2, that curve matches the curve of #1 while the house is occupied, but during the unoccupied times falls toward zero until it is time to get it back to Tin in anticipation of people returning home. It then rises back up to Tin.
The area under house #2's curve will be less than the area under house #1's curve.
Thus, in terms of energy required to produce the desired temperature curve, house #2 uses less than house #1.
There are inefficiencies in producing and applying that energy, though, and so getting a given amount of energy applied to heating or cooling the house from your heating or cooling system will take more energy, and that extra energy might depend on Tin or Tout, so it is possible that this might be a big enough effect to counter the savings from letting the unoccupied temperature move toward Tout.
This was my 400 level thermo 2 class, we calculated everything, inefficiency, convection, conduction.
From a pure heat capacity viewpoint, heating cooler air is very slightly easier (on the order of a few thousandths at most for realistic temperatures) [0]. Don't think it'll be noticeable for the average heating system, though.
> we calculated everything, inefficiency, convection, conduction.
I'd be curious to how those calculations affect things. If the heating element is the same temperature, I'd think heating cooler air would be faster because heat conduction is faster across a larger temperature differential and you'd get "faster" convective mixing for air with bigger temperature differences. Have to admit I'm not sure what inefficiencies might come into play, and I haven't taken classes at that level so I wouldn't be surprised if I missed something.
[0]: https://www.engineeringtoolbox.com/air-specific-heat-capacit...
So at least part of the efficiency comes from not restarting the fan repeatedly.
So the blower uses less than 3% of the energy used by the burner. Some of the waste heat from the blower motor probably helps heat the home, so in reality it's probably less than that.
While startup current is significant (for a very short time), starting the fan up in the morning and again in the evening after work doesn't add that much to the total power drain, or even cycling it on/off a few times an hour to maintain temperature. Starting wattage on that motor is around 1800W, but only lasts for a few seconds.
Based on my experience with most houses’ insulation, especially bigger ones, I cannot imagine it being economical to cool it for 8+ hours when no one is there (for work and school), rather than letting it warm and then starting the AC 30min before people start coming back home.
The AC will be more efficient in the morning, for one, than during the heat of the day. And if you let the entire house get truly hot inside, it will take a lot longer than 30 minutes to bring the temperature down (it's not just air that has to get cool, it's all the solid objects as well). And when it's fairly hot outside, it may not actually be possible to get it cooled down if you wait until the heat of the day. E.g. my AC will keep my house at 70F when the temperature outside is over 110F, but if I let it drift up to 80F inside and then try to bring it down to 70F in the mid-afternoon, it won't get any lower than maybe 75F until the ambient temperature outside drops into the 90s.
Also can't use a fan on the west coast in the later parts of the summer when the air is full of wildfire smoke.
Gosh I wish I could find it. I've referenced this problem a few times, I need to find it. I might have the book, if I can find it I'll update this post.
With something like this you'd need near constant cooling. Although still you are only cooling a small volume, so it could be better.