Fridge not cold enough… again

Hiya!
Started a tenancy early this month, the kitchen had a built in fridge/freezer and I noticed that the fridge was unusually warm, not only on the inside but also on the outside as it is enclosed in wooden frames with little ventilation despite having 2 holes in the back for ventilation (this is my opinion).
I set the fridge thermostat to the max to no effect.
I then bought a thermometer that showed a constant 13-15°C in the middle shelf.

I complained and the landlord said it was strange as the fridge was working fine until now… but it is 10 years old so he decided to buy another one, brand new, LEC T5039W, as was one of the very few models with a size that would fit inside the cabinet.
Today, 5 hours after turning it on, the thermometer is showing a constant 13-15°C in the middle shelf, AGAIN!
The freezer works fine (thermometer drops to -15°).

Do you think it makes sense to remove the fridge from the cabinet and see if it gets cooler? Anything else I should try? Any suggestions?
How likely is it that both fridges are actually faulty?