Thermostat overshoot

Why does turning the thermostat far above the temperature you want not heat the room any faster?

Everybody does it. You come into a cold house wanting twenty-one degrees, and set the thermostat to thirty, because surely a bigger demand fetches a bigger response. Then you forget, and two hours later you are opening windows in a room that has reached twenty-five.

The mechanics of a feedback loop — error, gain, the three classical terms, why too much gain makes a loop unstable — are worked through in Feedback control, so take that as given. The interesting thing about a house thermostat is that it has almost none of that machinery. It is the crudest controller there is, and the question is exactly what a setpoint can and cannot buy you in a system that simple.

So ask what the thermostat physically is. In a conventional heating system it is a comparator wired to a switch: it looks at the room temperature, compares it with the dial, and either closes a contact or opens it. That is the whole of its output. There is no third position, no half-open.

Which means the boiler, when it runs, runs at the output the boiler was built for. Not an output chosen from the size of the gap. So follow the consequence: the rate at which heat enters the room is the same whether the dial says twenty-one or thirty. Setting it high does not commission more heat. It only moves the point at which the heat stops.

But now an honest objection, because the experience does not feel like that. The room really does warm quickly at first and crawl at the end. Something is easing off — so is something modulating after all?

No, and this is worth slowing down for. The room is not a bucket being filled; it leaks the whole time, through walls and windows and draughts, and the leak is roughly proportional to how far the inside is above the outside. Cold room, small leak, and nearly all the burner's output goes into warming air and furniture. Warm room, big leak, and much of it goes straight out through the fabric. The net heating rate falls as you climb, so the approach is an exponential drift toward whatever temperature the loss finally balances the output — a shape produced entirely by the leak, not by restraint on the burner's part. And the dial does nothing to the leak.

So the high setting cannot speed the climb. What it certainly does is remove the stopping point: the contact that should have opened at twenty-one stays closed, and the room sails on.

Which raises the second half of the question. Why does a room overshoot even when the dial is set correctly?

Because the switch opens at the moment the sensor reads twenty-one, and by then a good deal of heat is already in flight. A radiator holds several litres of hot water, all of it still radiating after the burner cuts. A wet underfloor system is far worse: the screed slab is a heat store measured in hours, unloading into the room long after the demand ended. The sensor lags too, having its own thermal mass, and it sits on one hallway wall reading one point rather than the room's average.

That is thermostat overshoot: not a mistake in the controller, but the arrival of heat that was committed before the controller said stop. And the size of it is set by the emitter, not by the dial — which is why turning the dial high buys you the overshoot plus everything above your target as well.

Three refinements, one of which qualifies the whole account.

First, the qualification. "The setpoint does not affect output" is a statement about on/off systems, and not everything is one. A modulating boiler with load compensation, or a heat pump with a variable-speed compressor, genuinely varies output with the size of the gap. Even there the argument survives in weaker form: no system can exceed its own maximum, and from a cold start it is already using it. The extra you demand by dialling thirty is available only where the appliance was throttling back anyway — near the target, at the end. And on a heat pump the high setting is actively expensive, because a higher flow temperature lowers the efficiency of every unit of heat made.

Second, the dead band is not the swing. A thermostat is given a small band so the relay does not chatter around the setpoint. But the swing you experience is wider than that band, because stored heat keeps arriving after cut-out and the room keeps cooling after switch-on. The band is a design choice; the extra is lag.

Third, how the problem was solved is telling. Old mechanical thermostats contained a heat anticipator — a tiny resistor beside the bimetal strip, energised while the burner ran, warming the sensing element slightly so the thermostat cut out early. It worked by deliberately lying to the sensor, timed to cancel the heat still on its way. Modern electronic controls do the equivalent by cycling several times an hour with a duty that shortens as the room nears target.

How you could refute this. Two cold starts, same outside conditions, a thermometer in the middle of the room and a stopwatch: once with the dial at twenty-one, once at thirty. My account predicts the curves are indistinguishable all the way to twenty-one and diverge only afterwards. If the room got there meaningfully sooner on the high setting, the output is not fixed and my account is wrong for your system. Quicker version: put your hand on the radiator five minutes into each run — equally hot means the setpoint is not buying output.

• Why underfloor heating is usually run from weather compensation rather than a room thermostat.
• What the right dead band is, given that a narrow one saves comfort and costs relay life.

Every term the collection defines is gathered in the glossary.