Hi Jhuff8181,
Residential refrigerators are exactly the same as you'd find in a sticks and bricks home and they operate exactly the same. The difference in your RV is that the power can come from either your shore power connection, or from the batteries by way of the inverter and transfer switch.
Since the warming is common to both freezer and refrigerator, it sounds like maybe the compressor is not running reliably. There could be a problem with the refrigerator itself, or perhaps with incoming power.
The first thing I'd suggest is to check the 110V circuit breaker for the frig. If it's tripped, you'd be running off battery power and might be taxing the power converter's ability to keep everything running and keep the batteries charged. Also check the remote switch for the inverter to see if it shows any error codes when the refrigerator starts getting warm.
Our owner-written
Residential Refrigerator Guide includes a wiring block diagram that illustrates how the frig is powered. You may find it helpful in checking the power being supplied to the frig.