This is not true. It might seem that way because of how long it takes your house to warm up. There is no momentum or stiction with heat transfer. When the inside of your house is warmer than the outside you are losing some amount of heat to the outside proportional to the difference. Any heat you add to maintain that difference when you are not home is wasted. As long as you can tolerate a stone cold house when you return, your best efficiency is to just turn the heat off. This is assuming you have an on-off heating system, someone mentioned a throttling system is more efficient at a low flame rate so that made it better to leave the heat on low all the time. I am skeptical of that claim but don't have enough information
It seems intuitive that heat exchanger eff increases with decreased flow rate. Also air handling is always best done as slowly as possible, because you're trying to move air, not make noise and turbulence. There doesn't seem to be any intuitive reason to think eff would be higher at low rates unless its doing something insane like varying fuel/air ratios to get a desired heat flow or some kind of slow PWM with repeated ignition losses. Real furnaces don't work like that, so...
My otherwise boring furnace is variable speed and the longer its on, the faster it runs. It's really roaring after about 30 minutes. Its more than a decade old, this is pretty old COTS tech. My first zillion BTU cost me somewhat less than my last zillion BTU in any heating cycle.
I live in a cold northern climate with great insulation and low heating bills and a variable speed furnace and the house is basically never empty (spouse and I work at home often enough, etc). The whole "nest" idea doesn't work financially for me although it is interesting to watch.
That was me, with the throttling system. It's called modulation, and is very common in Europe.
While there is no momentum in heat transfer, the walls of your house store heat. If you're away long enough to allow your house to cool down it will take more fuel than it would to keep it at a reasonable temperature. Also, this is much, much more comfortable than to arrive in a stone cold house, only to open a window 30 minutes later because of the blazing heat.
I'm not saying it's always better to keep a certain temperature, though. It depends on the time that you're away, the insulation of your house, the outside temperature, the efficiency of your boiler, etcetera. But, having lived in houses with ordinary thermostats and non-modulating boilers and houses with programmable thermostats and modulating boilers I can tell you this: I'm not going back to the old stuff. The indoor climate is so much better now!
