Thermostat
Item
This is a thermostat. It looks kinda like the classic round Honeywell thermostat (without the branding), and if you stick it on the wall of a room (more on that later), it will control the temperature in the room.
Instead of graduations, the Thermostat has a blue-red gradient that you position the needle along. The temperature range can vary by Thermostat, but generally speaking, you’re looking at a range of cold fridge to hot sauna.
When you place a Thermostat and set it, the magic exerts energy to make the room’s temperature more in line with what the thermostat says. This works similarly to a conventional furnace/air conditioner. The magic detects the temperature of the room. If it’s too cold, the magic spends energy to warm it up. Too hot? The magic spends energy to cool things down. Just like with a real thermostat, it takes some time, at least a few minutes, for the temperature to adjust.
Other factors can affect the temperature of the room, of course. An open window is the easiest example. Things like that will make the Thermostat’s job harder, but it will persevere.
Regarding the sticking of the thermostat to the wall, it feels like a moderately strong magnet to pull the thermostat off the wall and stick it back on, but it’s not magnetic; it’s magic. When I say “moderately strong”, I mean stronger than a refrigerator magnet, but not so strong that it’s actually difficult to pull off the wall with your hand. The force required to remove a thermostat varies from person to person and room to room.
When you place a thermostat on the wall, you’re basically making a proposal to the magic. You’re proposing that the “wall” (whatever form it takes) is part of a “room” (whatever form it takes) that the Thermostat can affect. If you try to use the thermostat in a way that is not valid (like if it’s too big a room, or it lacks sufficient cohesion for the magic to consider it a room), then it simply won’t stick. Adjust your environment (or find a new “room”) and try again. It’s a case-by-case, and it’s not consistent across different thermostats. Some might work in some “rooms” where others might not. Some might consider certain areas to be a part of the “room” where others might not cover those areas. You’ll just have to try it and see. That said, it’s usually pretty obvious whether or not something is a room, and in nine out of ten cases, using a Thermostat is perfectly straightforward.
If there is more than one thermostat placed in a single room, only the first one placed will function. But then if you pull that one off, control passes to whichever of the remaining thermostats was placed first.
Temperature changes are magical rather than physical, so in a room with a Thermostat installed, hot or cold temperature shifts will not happen outside of the confines of the room. This can lead to abrupt temperature shifts when entering and leaving the affected area.
Ethan Abides 
Are there upper or lower temperature limits? Will connected rooms also become that temperature? What about adjacent rooms with a door open?
Will it work in a room with no ceiling?
If I put it in my bathroom and then try to take a hot shower will the shower stay the temperature of the room? Does the answer change if the thermostat is placed inside of the shower?
In order.
The range goes from cold fridge to hot sauna, roughly. There aren’t degrees on it, there’s a blue to red gradient. Adjust until you’re comfortable.
No, just the room with the thermostat is affected. This can cause abrupt temperature shifts if you leave or enter the affected room. Ventilation doesn’t matter. Open door, open window, open skylight, whatever. That said, outside forces can still affect the temperature. In the hot shower example (okay, I guess not “in order”), your shower would heat up the room, and the thermostat would work to cool it, but it wouldn’t be instantaneous. If you have the window open and it’s winter, that can cool down the room, and the thermostat would work to warm it back up, but again it wouldn’t be instantaneous.
So in that sense, ventilation matters. Ventilation does not matter when determining the dimensions of the room. And you don’t get to pick those yourself, incidentally; the thermostat does. You stick it to the wall, and whatever the thermostat thinks the room is, that’s what’s affected. You’re not always gonna know if something’s gonna work or not.
So I don’t know if you need a ceiling or not. Try it and see. If the thermostat sticks to the wall (or whatever you think is serving as a wall), then you’re good to go. It’s a case-by-case, and it’s not consistent across different thermostats. Some might work in some “rooms” where others might not. Some might consider certain areas to be a part of the “room” where others might not cover those areas.
It’s just gonna depend on your shower stall and the thermostat itself whether or not it would be considered its own “room” if you placed the thermostat inside it.
I think that covers all your questions. If I missed one or I’m inconsistent, bear in mind I wrote and published the Thermostat last night after 3am, and I’m operating on six hours of sleep. Which is less than normal for me.
I just looked at the write-up itself again, and yeah, inconsistencies. I’ll need revise and republish, probably. Thanks as always for your help.
Okay, I’ve put up the new version.