Dometic rm 2310 fridge not cooling - Dometic RM2193 Compact Refrigerator With Ice Box

SOURCE: Dometic RM2652 Refrigerator Problem

Check the flu at the back is clean

SOURCE: I have a Dometic RM 2652, the freezer works fine.

Here is the trouble shooting manual for your Dometic.

http://www.gasrefrigeration.net/dom_techdata/26121_2852SM.PDF

It will tell you what the possible problem is.

SOURCE: Camper fridge dont cool

I also had the same Model Make. I removed my fridge and placed it upside down, occasionally shaking fridge within a 24 hr period. This seemed to re-mix the ammonia solution and the fridge is working.
This may work for you but look for yellow stains if you see any your fridge is leaking and would require repair.

SOURCE: Dometic Rv fridge will get cold on a/c power but

does the flame ever got out if not ,the tsat is not the problem. It could be that the flame is not hot enough or the flue has a restriction

SOURCE: I have a Dometic RV fridge that wont get cold. it

It sounds like your cooling unit is going out. Here's a couple of things to check. Do you smell any ammonia when you open either one of the doors? When you look at the rear of the fridge, do you see anything that looks like rusty water that has run down any of the metal tubes and dried up? If the answer to either one of these is "yes", then youll need to start looking for a new fridge or replace the cooling unit on the one that you have.