I think the key word you used is STABILIZE. You want to make the inside of the box stabil when the outside is changing seasonally or even nightly. The answer is INSULATION
. That could mean anything from rebuilding your box to simply fixing lid seals
. Your "control unit" is only responding to the fluctuating temprature it sees.
And when ice builds up on the evaproator, defrost. All that ice is counter productive to keeping things cold. I know that does not sound right, but trust me.