Re: Does it really save that much?
"You drop the thermostat to 15℃ when you are out. Eventually, your house will get to 15℃ and your heat loss rate will be two thirds of what it would have been. But, until it gets to that temperature the reduction of your heat loss is less than a third. And when the heating goes back on, it has to work harder to raise the temperature of the house."
That sounds suspiciously like the common argument that "if you turn the heating off, it uses more energy to warm the place up" which is simply untrue (and in any event, a higher delta on the primary and return heating circuits would actually make most heating systems MORE efficient, not less). Unless you've got a poorly insulated high thermal mass house, then any half decent boiler can easily warm the house up in a few minutes, and there's no reason to set it for 15C when you're not there - why pay to keep the cats warm when they've got fur coats? In a well insulated house even turning the heating down by a few degrees will cause the boiler to turn off for a fairly protracted length of time, so you wouldn't be using gas at two thirds the rate you were in your example, even though that would be the case over a more extended time period. Potentially 10-15% of your total heating bill is being spent on eight hours a day or so of 15C heating of an empty house.
A well set up heating system should (typically) see the CH go off twenty minutes before the house becomes vacant. With perhaps sixteen hours of daily occupancy, that twenty minutes is 2% of your space heating energy use. If the system is properly configured, then it would come on ***just*** in time to raise the temperature to the desired level for occupants coming home. If that's only ten minutes difference, you've saved another 1% of your heating bill. Now, if you vary the heating by time of day when you're in, then you're probably cutting around a further 7% from your heating costs (when you're active you can run a lower temperature and still be comfortable).
You can do all this yourself with a dumb-ish programmable thermostat and time (I've had this for two decades), but it's a pain to set up. A good smart thermostat will do all of that for you with minimal effort, and for many people can save more than 20% of their heating costs for no change in comfort. Stuff the tree hugging issues, and look at it as an economic and practical investment, and there's relatively few scenarios where a smart thermostat doesn't make sense, particularly if you do your research and avoid the crummy "me-too" smart thermostats rushed to market by some makers. Arguably the optimal solution is a Nest. Install, let it get settled in, then when it is working to your satisfaction stop it connecting to your wifi if you've got privacy concerns.