Start with reading refrigerator sticker.
The 12V element is rated for much less power than 120V element.
I post my test somewhere on this forum about my Dometic and 120V and gas had almost the same performance. Gas run like 2 degrees colder, but that could be within error margin.
Standard truck plugs are rated for 30 amp when big fridge is rated 18 amp.
Lance idea might be overkill, but usually weak point are the plugs. They are build cheaply and often neglected, so making bigger connection is never bad idea if you want to spend time on it.
Would I make new connection, I would make it >100 amp rated so I could use my dual truck batteries for fast inverter/microwave use on the road. That also would allow me to run fridge on 120V for full output.
For me, driving in 110-120F weather now the 12V is just not giving enough cooling power.