Last spring, I bought a mobicool soft cooler. I removed the cooling unit from the bag and installed it on the lid of my icebox (more than 6cu.ft.). This unit is running full time when my boat is at dock, it's powerful enough to cool the icebox form 10 to 15 celcius down from the ambiant temperature.
Also, the ice last longer with that cooling unit. This kind of cooling unit as a very low efficiency so it could be hard on the batteries.....but at dock, it's fine.....for the price!