Try running your refrigerator in LP mode in very hot weather. You probably don't need the extra complexity of a 12v fan.
These are, after all, LP refrigerators with secondary, less efficient electrical heaters. Electric is usually good enough but in hot weather you may need the extra cooling the extra heat LP provides. 25% more cooling is not uncommon. Compare the power used in either mode.
My Dometic has a power use of 324 watts on 120v and 439 watts on LP. The electric is only 74% of the LP's heat (assuming perfect efficiency).
Your refrigerator will run a month on one cylinder of LP so no worries there.
-- Chuck