Bosch integrated fridge thermostat

I have an integrated Bosch fridge with no discernible model number/serial number, either on the outside or inside, so apologies for not being able to supply these.

The fridge is around 9 years old but recently I noticed the contents weren’t cool enough. So, I bought a fridge thermometer and discovered it was running at 10 degrees instead of the recommended 2/4 degrees. The control was set at 2 and so I increased it to the maximum 5 and that’s reduced the temperature to a more satisfactory 4/5 degrees.

My question is, would replacing the thermostat (which I hope is situated inside the control unit) improve the control range of the that item, or is the maximum reduction in temperature I’m getting due to a more serious deterioration? It’s just that my minimal research leads me to believe that a thermostat either works, or it doesn’t. So, given that turning mine up to the max has improved matters somewhat, I’m wondering if replacing it would be a waste of time and money.

Thanks everyone!

David