I have a wireless thermometer in my fridge that also shows me the high and low. I normally see a high/low range of 33 to 38 F in the box. I believe that a variation is normal. That absorbtion cycle takes some time to start removing heat once the thermostat/controll board recognizes the box needs cooling.
I did have a problem last year with the box getting to 44 to 46 F while on LP. It also took a long time to cool from a warm start. After doing all the required jet cleaning, burner cleaning, flue cleaning I found the problem was low gas pressure and a slightly lower that normal flame. I made a homemade manometer and with some clear plastic tubing and found the pressure was 8 inches WC when it should be 11 inches WC. I replaced the regulator and now the box cools better on LP than electric.
.... just some things to think about.