I have long been a supporter of having an internal temp reading method for your frig as it is just good safety sense and also an indicator of some kind of failure happening. I will also say, though, that the thermometers can cause you to over react to stuff regularly.
We have had compressor frigs for many years now so have a very consistent setup. I prefer the mechanical thermostats that control on or near the freezer box a it gives us a good balance of frig and freezer control and with a wide enough hysteresis to not over cycle.
What we have found over the years is that any temp issue we have in frig is generally not related to the frig itself and the frig is doing just what it should be. Many/most of us do our initial testing without food in the frig and it either empty of some heat "ballast" like a six pack or gallon jug of liquid in it.
Then problems show up after a while on the road, with the temp rising somewhat. We commonly see sudden jumps to 42-47* in our frig sometimes which is about 10* higher than our normal temp.
The first instinct is to mess with the thermostat, but that is often inconsistent in results for us. The problem is inevitably that the food has bounced around a bit and is shielding the temp reading (not controlling) sensor in the frig. Move a bag of cheese or whatever 1" and the temp quickly returns to normal.
When we put in a new frig a couple of years ago it had an electronic control that sensed in the frig with the sensor on the rear wall and it had the same issue, but on steroids because it was controlling the cooling. We constantly had horrible temp swings in the frig. We do have a couple of little fans in ours to direct air around inside the box, but they aren't a total cure all if you have a bunch of stuff in the frig.
So, I think the bottom line is to do your testing empty or ballasted and if it comes out good don't over react to the reading from an add on sensor. Rearrange the food first, especially if the increase comes on quickly or after driving or shopping for groceries. Many of us over pack our frigs and make all of the issues worse because of it.