A word of warning: I have had a rather broad scientific education, and I like physics. The following is a discussion of Newtonian Thermodynamics, observation, energy exchange, and beer. If you don't have the patience to read it, you can skip to the last paragraph, which contains the actual point.
As brewers, we heat and cool beer regularly. It is part and parcel of the brewing experience, and a major factor in how the beer turns out. It is a most fundamental part of brewing. It is also a lie.
It's a lie because this is not actually what were doing. What we are doing is applying energy to a system in order to affect a change in the energy state of a system. Put simply: We don't heat or cool beer, we do things to the environment the beer is in, in order to make it hotter or colder.
This may seem like a petty distinction, and in the case of heating beer, it generally is: When I put a heating element in a vat of beer and turn it on, I'm heating the beer. (At least in any Newtonian sense of the word). But in the case of cooling the beer, this is actually something worth considering: When I cool beer, I don't take energy out of it. I don't aim a "Cold Ray" at it. I put it in the fridge. I change the temperature around the beer, so that the temperature of the beer changes.
And this is important because when I measure the temperature of the beer, I don't actually measure the beer. I measure the temperature of the environment the beer is in. When I tape a sensor to the fermentation bucket, the reading I get will be an average of the temperature of the bucket, and the temperature around the bucket. It will NOT be the temperature of the beer.
Now presumably if you leave an object in an ambient temperature for long enough, it will end up being in ambient temperature. You can try this with a simple experiment: pour a glass of ice water and leave it on the counter. It will eventually warm to room temperature. So be extension, if you had a thermostat next to the glass that showed the room temperature, it would also show the water temperature, since they end up the same.
But beer doesn't work that way. Beer ferments, and fermentation is an exothermic process - it creates heat. Leave a bucket of fermenting beer on the counter, and it will not reach room temperature, because it makes its own heat.
It gets worse: If you tape the sensor of your thermostat to different spots on the bucket, you will get different readings. This is true because beer, like any liquid, stratifies according to density and thermal layers. Moreover, if you tape your sensor to the lid, which does not come into direct contact with the beer, you will get a reading that's much closer to the ambient temperature than the beer temperature.
Now do a little thought experiment: Lets say that you have beer that is finished fermenting. You fill a bottle with it, put both bottle and fermentation bucket in the fridge, and tape the sensor to the bottle. How close is your reading to the temperature of the beer in the bucket?
The answer is, you don't know. Your bottle may cool faster because it's a smaller thermal mass. It may read cooler because it's further in the back of the fridge, or because glass is a better thermal conductor than plastic. It may read warmer because the curve of a glass bottle is bigger than that of a bucket, so the surface area in contact with the sensor is smaller. You simply don't know.
All of this comes by way of saying something simple: Two days ago, my beer was in secondary fermentation, at temperature of 11.5C. Now it's heading toward lagering, with a temp of 8C and falling. I didn't touch the beer. All I did was to change where the sensor was located. So I don't know what temperature my beer is really in, and what temperature was it before. And it's kind of driving me nuts. :)