Can I diagnose/fix problem with my Iceline Deluxe Frost Free freezer?

It's an Iceline Deluxe U7 95 77, bought in the UK about 12 years ago. It survived 2 house moves, but we were then forced by another house move to shift it and leave it switched off for about a year (yes I know we deserve to have trouble!).
It now runs, and the red temperature warning light comes on, but the air it's blowing into the cabinet isn't cold.
Reading around on the Internet, it seems that it may be a problem with the thermostat - can anyone confirm this, please? Any other likely culprits? Any clues about testing to diagnose, and likely cost of spares? Any info gratefully received, and if I can fix it I promise to be kinder to it in future!