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I would say it should warm up faster because the difference in temperature between the room and heater is higher.

Edit: I am talking about a convection heater.

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    $\begingroup$ To answer your question with a question: why would you want it to work like that? Artificially not warming as fast as its able to when the error is only small $\endgroup$ – Richard Tingle Dec 8 '17 at 16:57
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    $\begingroup$ Any heater that did that would be poorly designed. If I really want the room to reach 70 degrees as quickly as possible, I have to set it to 90 degrees, then wait until it hits 70, and then set it to 70? If I wanted to have to watch the temperature and change things based on it, why do I have a thermostat? $\endgroup$ – David Schwartz Dec 8 '17 at 19:14
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    $\begingroup$ There's an interesting paper ("Two Theories of Home Heat Control", Kempton 1986) which studies the mental models that people develop about how thermostats work. The data is sparse, but the author estimates that 25% to 50% of Americans believe setting a higher temperature will heat up the room faster. $\endgroup$ – David Dec 8 '17 at 21:12
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    $\begingroup$ If it's a two stage unit, it will. But usually not because it's set higher. It will switch to the 2nd stage if it runs long enough. $\endgroup$ – Mazura Dec 8 '17 at 21:58
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    $\begingroup$ @AnthonyX when I posted this question I thought the explanation would be physical rather than "a thermostat doesn't work the way you think it does". $\endgroup$ – Limechime Dec 10 '17 at 16:46
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Because you're only changing the temperature at which the heater is supposed to stop working.

It is always working at the same power, regardless the temperature difference. But for higher temperature it will have to heat at this same power for longer time.

So in short: You don't change the difference in temperature between heater and the room.

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    $\begingroup$ Oh, that's what I got wrong all the time. I was assuming the heater would heat at a higher temperature when I put the thermostat on a higher setting until that temperature was reached. I didn't know heaters would always run at maximum power regardless of the setting. Thanks for clarifying. $\endgroup$ – Limechime Dec 8 '17 at 12:42
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    $\begingroup$ @Limechime The same is generally true of microwaves as well. When you set a microwave to 50% power and 3 minutes, it's not actually running at 50% power continuously for 3 minutes, it's running at 100% power only 50% of the time, generally alternating between off and full on for ~15 seconds at a time; which usually results in the sound the microwave makes changing every time it switches on/off. $\endgroup$ – Shufflepants Dec 8 '17 at 15:00
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    $\begingroup$ Many things, including heaters, microwave ovens and air conditioners use a very coarse-grained binary Pulse Width Modulation technique. The heating element / magnetron / compressor is either off or on. The control mechanism turns it off (multiple seconds or longer) and on (multiple seconds or longer) to achieve the desired temperature / power level. This is something Dr Fred Brooks calls out in "The Design of Design." Most people do NOT understand this. Once they do, many behaviors no longer make sense (turning the AC colder, trying to cool off the room faster, etc.). $\endgroup$ – Meower68 Dec 8 '17 at 15:09
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    $\begingroup$ @Limechime: Think of it this way: If I put the pedal to the metal, my car will accelerate at the same rate from 0-100 km/h, regardless of whether I'm trying to reach a top speed of 100 km/h or 200 km/h. $\endgroup$ – Flater Dec 8 '17 at 15:18
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    $\begingroup$ Another appliance where this happens to calamitous effect is regular ovens. $\endgroup$ – Stella Biderman Dec 8 '17 at 17:28
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The thermostat in a heater is usually an on-off device. It senses the room temperature and runs the heater at full power as long as the room is colder than the target temperature. If the room is hotter than the target temperature, the thermostat turns the heater off.

(In a narrow temperature interval around the target temperature the thermostat will usually stay in the state it had the last time the temperature was outside the target interval, such that it won't incessantly turn on and off based on fractions of degrees of difference).

Your description sounds like you're expecting the thermostat to be based on the temperature of the heating element inside the heater, but manufacturers do their best to avoid that and instead let it sense the actual air temperature in the room, since that it what you as the user actually have a preferrence for.

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  • $\begingroup$ I always got the last part wrong. I thought turning up the thermostat resulted in the heater being warmer while warming up the room until a certain temperature was reached. $\endgroup$ – Limechime Dec 8 '17 at 12:47
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    $\begingroup$ @Limechime Some control systems are like this; that is, the bigger the error signal (in this case the difference between the thermostat setting and the actual temperature), the harder the controller drives the correction, with the drive becoming more relaxed as the error lessens. But heaters are generally not like this; one wants the error corrected as fast as possible (the room has to get to the wished-for temperature as soon as it can) and that means that the heater drives as hard as it can. Minimizing error as fast as possible is not always desirable: it can give rise to unstable dynamics. $\endgroup$ – Selene Routley Dec 8 '17 at 13:40
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    $\begingroup$ Though some more high-tech furnaces (such as the Lennox I had installed a few years ago in my home) have a variable heat output based on input from a smart thermostat, and do change the amount of heat coming out depending on how much of a difference there is between the set point and actual room temperature. So while close to the set point, my furnace runs at a low heat, but if I adjust it to be several degrees different it will ramp up and run at a higher heat output until it gets close to the setpoint, then it will ramp down to a less intense heat output. $\endgroup$ – Milwrdfan Dec 8 '17 at 15:29
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    $\begingroup$ Which heads you into the world of PID controllers (or their digital counterparts). Proportional: the further you are away, the harder you try to get to the target (but for a heater this clamps to the maximum output pretty quickly); Integral: removes a "fixed offset" error that is common for proportional alone; Derivative: dampens oscillations above and below the target value (see PID on Wiki). $\endgroup$ – TripeHound Dec 8 '17 at 15:48
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    $\begingroup$ I have a free-standing heater that senses the temperature of the heater, so turning it up higher does actually make it heat the room faster. I imagine that's typical of free-standing heaters simply because there's nowhere else to put the sensor! $\endgroup$ – user253751 Dec 10 '17 at 23:59
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To add to the otherwise good answers...

The OP says in an edit that they are only talking about a convection heater. If the heater only has one heating element, then the answers about when the thermostat turns off are broadly true.

If the heater has multiple heating elements though, you can turn on more of them. Old-fashioned electric fires in the UK typically had up to 3 heating elements. The more heat the fire puts out, the faster you'll get up to temperature.

The same principle applies to central heating systems too. Most boilers allow you to set the temperature of the water circulating round the radiators. If you increase the temperature here, all your radiators will now be hotter and rooms will heat up more quickly. Do be warned though that this can be a real safety hazard, especially if there are small children in the house.

This does assume the air from the heater is evenly mixed around the room, of course. This is not always true, if for example you have a small heater in a large room. In this case you may want to turn the thermostat to maximum until the corners of the room are broadly warm, and the centre of the room is too hot. You can then reduce the thermostat to a more sensible "steady-state" temperature, and allow normal air circulation to even out the temperature.

Note that by doing this, you are technically applying "feed-forward control" - with a control system which doesn't quite deliver what you want, you're tweaking the control system's setpoint now to allow for what the system should be doing in future.

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In addition to answers, I simulated an example setup to show the differences. In your case, only the referance value of the controller is changing.

I have trouble with imgur, so I also posted images online.

Model: https://s18.postimg.org/71vo9wq0p/image.png

Plot: https://s18.postimg.org/rm0i8el7d/image.png

Comparison: https://s18.postimg.org/4xbb8tw3t/image.png

Model Plot of temperature Comparison of 2 different referance values

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