I had a similar problem with our Dometic 8 cu ft fridge. Blue flame and all. After 2 years of having temperatures rising in fridge part when on gas. I saw a post that mentioned that you should be able to hear the burn when running on gas. I could not. There are 2 things that need to be checked. LP pressure is first. I had a Mobile RV tech do this. Then I removed nozzle/orifice from burner. Soaked it in Alcohol for 1/2 hour. Then blew it out with air. Installed nozzle back in place. Fired fridge back up. I can now hear burner when flame is on. Temperatures are now below 40 on a lower setting than I used before.
Hope this helps.
Someone else may have information on how to check/adjust LP pressure yourself.