There are in Europe a set of temperatures which have different names given to the appliance.
Cellar or wine storage is at 12°C
Refrigerator is at 5°C
Often compartments within the refrigerator are given star ratings.
0 = 0°C
1 = -6°C
2 = -12°C
3 = -18°C
Freezer is at -18°C.
Some fridge/freezers have a holiday mode for the fridge where the temperature in the fridge is allowed to rise to 15°C. But the fridge range is normally around 1°C to 7°C. Since the same motor runs the fridge and freezer to get into the electronics and alter the range would not be easy. Some do have solenoids which allow the fridge and freezer to run at different temperatures others the two are tied together so altering the fridge would also alter the freezer.
With very simple units there is just a thermostat and only two connections and there is really no reason why that could not be replaced. Others have complex systems and you would really need to reverse engineer it to alter it.
However in the UK many home brewers take a standard fridge and use it to brew with at around 20°C. I used a
MH1210A temperature controller to do this and I decided to build it as a stand alone unit and just plug the fridge into the stand alone unit with a sensor just placed in the fridge.
You may be able to build it into the fridge but either way the main point is you can then set any temperature -40 ~ 120°C.
The problem is stopping the unit from overshooting or trying to restart before the gases have equalised causing strain on the motor. The one I used allows you to set a time delay to stop this. When using with a freezer I found 1.5°C between on and off limits worked well. Timer is to stop it starting every time door is opened. Most brewing guys use a STC-1000 controller as they want both heat and cold to be controlled but not seen instructions don't know it they have delay timer.
As to building in or free standing I found with the freezer using the pocket for the sensor means it is not as effected by opening the freezer door.