Six LEDs at 350 mA isn't a lot of heat, only 6 watts or so. For a small plastic enclosure, that might be a lot, but if the enclosure is metal, or larger, it's probably doable by mounting the LEDs on a heatsink inside the box. Of course, it depends on the outside temp. If it's going to be on when the sun is beating on it, and might get to 150 or 200F, nothing is going to work very well.