I think I understand what you're saying now. In vacuum, an object will radiate until it reaches absolute zero; in air, however, you're constantly being heated t

I think I understand what you're saying now. In vacuum, an object will radiate until it reaches absolute zero; in air, however, you're constantly being heated to the ambient temperature, meaning you can't radiate your way down until the air has lost its heat too. The thing I think you're not taking into account is that this device has the effect of slightly increasing your black-body radiation. So you're at 1300K, radiating at 1300K, but we apply a little electricity and you start radiating a little more-- maybe you now look like you're at 1301K. Your heat hasn't actually increased, just apparent radiation, and as a consequence you cool down a little faster than your black-body profile would suggest. So say you're at room temperature, radiating at room temperature, being warmed by the air, and not losing any heat. We apply current again, and you start radiating at a little over ambient temperature. The air is still warming you, but you're cooling a little faster than before, with the extra heat being deposited wherever the radiation is absorbed. To the air, you now feel cool. Why should the absolute temperature of the ambient air have an effect on the process?