Three settings, not one

The single most common arrangement is one temperature left alone all winter, and it is the one that costs most for the comfort it delivers. You are paying to heat an empty house during the day and an unoccupied living room overnight.

Three settings covers almost every household:

Then two overrides:

The setback arithmetic

Heat loss from a building is roughly proportional to the difference between inside and outside. That single fact explains why a setback works and why its value changes through the winter.

Hold 20 °C when it is 10 °C outside and you are maintaining a 10-degree difference. Drop to 17 °C and the difference becomes 7 — you have cut the loss by about 30 percent for those hours.

The same 3-degree setback on a night at −5 °C takes the difference from 25 to 22, a cut of about 12 percent. Proportionally less, but of a much larger number, so the absolute saving is bigger.

Why the same setback is worth different amounts. The percentages are the reduction in heat loss during the setback hours.
Outdoor20 °C held17 °C setbackLoss reduced by
10 °C (50 °F)10 °C difference7 °C difference~30%
5 °C (41 °F)15 °C12 °C~20%
0 °C (32 °F)20 °C17 °C~15%
−10 °C (14 °F)30 °C27 °C~10%

The figures are simplified — they ignore thermal mass, solar gain and how long the reheat takes — but the shape is right, and the practical consequence is real: setbacks earn their keep most in mild weather. Which is convenient, because mild weather is also when giving one up costs nothing.

The floor that outranks the saving

Everything above is about money. This paragraph is not.

Below about −6 °C (20 °F) outdoors, the risk stops being discomfort and becomes plumbing. The pipes in your walls, voids and unheated spaces are protected by heat leaking out of the heated rooms, and an overnight setback is a deliberate reduction in that protection at exactly the wrong time.

So: on a night forecast below −6 °C, hold the daytime setting through the night. You give up a few pence and remove the one risk on this page that comes with a four-figure repair bill. The reasoning behind the threshold, and what else to do on those nights, is in what temperature pipes freeze at and how to keep pipes from freezing.

For an empty house the equivalent rule is the 13 °C floor, and it does not bend. Most serious burst-pipe damage happens in properties left cold and unattended.

Turning it up does not heat faster

A thermostat is a target, not an accelerator. Setting 25 °C to "warm the house quickly" makes the boiler run past 20 °C and overshoot; it does not get to 20 °C sooner. The only lasting effect is that you forget, and heat the house to 25 °C all evening.

Getting more from a lower setting

Every one of these lets you hold a lower number at the same comfort, which is a better trade than any schedule:

Putting a number on your own saving

The percentages above are generic. Your saving depends on your bill, your setback, your hours and your building, and those are exactly the inputs the thermostat savings calculator asks for. It shows its arithmetic, so you can see which assumption is doing the work rather than trusting a headline figure.