Some fridges can be quite marginal...
- Some require the bottom "vegetable & debris bucket" to be in place and a shelf set correctly
- Others do not like working unless there is something in there to cool
The only way to really know fridge temperature is a glass of water & thermometer. It should really be no more than 7oC and the ideal is around 5oC (although certain foods have more specific requirements like cheese, lettuce, and so on).
Critical maintenance is preventing the rear fridge cool plate from icing up - on some slimline Indeshit this basically makes the fridge temperature climb inexorably away from safe levels. Common failure modes of fridge freezer is for the thermostat to fail - in some cases jamming on (usually noticed by =A3120+ increase in electricity bill and paint burnt off a very rust-orange compressor).
Measuring air or object surface temperature is pretty pointless. This not withstanding a professor moron of john moores was observed jumping around on BBC television news after "discovering" that surface temperature of objects rose markedly when the door was opened. Within even 1 millimetre of the objects surface the temperature was of course quite normal. I guess he also believed insulation was perfect too. Quite how he got an O-Level in physics never mind a professorship is beyond me.
I might be the odd one out, but I think all fridge/freezer manufacturers *should* be forced to provide LED temperature displays for both. I suspect they have not purely because many products are actually quite marginal with either minor ice build up (and never mind the fun of frost free). Alarms could be an lucrative optional plug-in extra like a card, SMT piezo & bit of logic - like a big SD. Can not understand Bosch putting the green/red lights behind the door seal so you can't see them without opening the door. Genius. They do have a dial thermostat in the door which has ambiguous markings.