I had a peltier cooled coolbox. It easily maintained a 25°C (45°F) differential and didn't take that much current (can't remember but it didn't worry the car battery).
Let's do some calculations,
A box of 1m x 0.5m x 0.5m and a wall thickness of 25mm of styrofoam would have 2.5m² of wall area. At an Rsi value of 1.25 it would require 2.5/1.25/1 = 2W per °K to cool it. So for a temperature differential of 20°C (36°F) would require 40W of cooling. Two reasonable sized units would easily suffice. An aircon unit would be total overkill.
Note, the R value is in m²·K/(W·in) hence 25mm = 1".
Edit, two of
these should manage to move 60W at a 20°C differential and use 8A at 12V.
Mike.