zut-
In a modern furnace, the heat exchanger is warmed up before the main fan is turned on, and the flame is at (basically) the same temp whether the furnace runs for 1 min or 1 hour. While warming the indoor air from (in this example) 66F to 72F, there is a slight improvement in the amount of heat transfer because of the slight increase in differential temperature (practically negligible). But, less fuel is wasted in the process of warming the heat exchanger once to run for a long while as opposed to warming the heat exhanger repeatedly when the furnace runs in short on-off cycles.
peace
If your furnace is only running 4min/hour to keep your house at 72F when it is 20F outside, you have a pretty well sealed, well insulated house. That has as much (or more) impact on the overall efficiency of the heating & cooling system than varying the T-stat a few degrees.
As far as estimating the savings: to simplify things, we will assume that all of the losses are due to conduction through the walls & convection at the outer surface (ignore radiation cooling- it is not that significant overall, but varies with the fourth power of the temperature difference, greatly complicating this simple estimate). All other things being equal, the heat loss will vary (about) directly with the temperature difference. In this example (20F outside, 66F or 72F inside), we have a differential temp of 46F vs. 52F. For a 66F setpoint, there will be about 12% less heat loss, so 12% less energy is used making up for this heat loss. The energy used to heat the house up to 72F from 66F will be less than the energy to maintain 72F, if the T-stat is left at 66F for the house to actually cool to 66F by heat losses.
Disclaimer: This is extremely simplified. The actual heat loss at the outer surface is not directly linear & differential equations are involved. But this is close enough for General Questions.
DDG-
If you like to bundle up at night and the house is occupied during the day, turn the T-stat down at night. Personally, I don’t like to be all bundled up when I sleep, and the house is empty during the day, so I have my programmable T-stat set to 60F at 8AM-4:30PM (not there), 70F at 4:30PM-8:30PM (warmed up when I get home, still warmly dressed), 74F at 8:30PM-12AM (winding down & going to bed, less warmly dressed), and 70F at 12A-8A (safely tucked in bed, and warm enough to get out of bed in the morning). This is done with a $60 programmable T-stat. Compared time when I had a normal T-stat and didn’t vary the setting, it saves about $15 a month in the winter. The big savings come in the summer here in Texas. Using a similar (but reversed) varience in the settings for summer saves a metric shi_load of money in electric bills (the T-stat pays for itself in a month if you don’t vary the settings, or slightly longer if you occasionally forget to vary the settings on your way out of the house).