You can get passively cooled 150W inverters, but yeah, a black box outside in the desert may not be ideal. You can eliminate most of the radiant and some of the convective heating with a beach towel on the box and an umbrella+emergency blanket above it. (I mean, we are talking burning man, after all)

If you seal your box in a humid environment, the cool night temps can cause condensation, so ventilation of the box would be useful to prevent this (as well as provide for active or passive cooling of electronics) or throw in some silica gel packs.