This isn't necessarily true. During a really active fermentation the fermenting wort is churning quite a bit, so when the most exterior liquid is being cooled it's transferring that temp. pretty quickly throughout the vessel. And if you have a fermenter you aren't actively cooling or heating, all the liquid whether in the middle or exterior is basically identical in temperature.
Actually, it is necessarily true. Even when the beer is churning there is a boundary layer between the rapidly moving wort and the inside surface of the fermentation vessel. There is essentially zero movement of the beer at that surface, and there is a lot of shear going on in the boundary layer. The inner limit of the boundary layer is where the fluid is moving at the same speed as the bulk. There will still be a thermal gradient across this boundary layer. The more convection inside the fermenter, the thinner the boundary layer will be, and the steeper the temperature the gradient across the boundary layer will be.
There is also a temperature gradient across the wall of the fermenter. With the temp sensor on the outside of the fermenter, the best you can do is measure the temp at the outside surface of the fermenter, which will be cooler than the inside surface. So, the beer will be warmer than the temperature you measure. The better the insulation on the outside of the temperature sensor, the lower the temp gradient across the fermenter wall will be, and the closer the measured temp will be to the beer temp. In the limiting case of "perfect" insulation of the temp sensor, the measurement would be equivalent to having the temp sensor in a thermowell in the beer inside the fermenter.
What people have found is that fermenters with thermowells have larger under (and over) shoots in temperature, than fermenters with somewhat insulated temp sensors on the outside wall of the fermenter. The reason for this it that with the thermowell, or too much insulation, the temperature of the chamber undershoots the set point more, so that when the compressor turns off, the chamber is even colder so the beer looses even more heat as the beer and chamber come into equilibrium. So, you really don't want to over insulate your taped on thermometer.
The above applies to heating as well, just with everything in the opposite direction.
The under/over shoot is an inherent characteristic of simple on-off controllers. To avoid over/under shoot, you need to use a controller with predictive capability, the classic example being a PID controller. With modern control algorithms and small, cheap computers, it is possible to create controllers that achieve even tighter control than PID's.
Brew on
