Infrared radiation in the atmosphere


Just out of curiosity, I stepped outside today during a clear day and I pointed my infrared thermometer up to the sky. Though sky overhead was totally blue, the thermometer gave readings between -34...-38°F. Air temperature is +33°F. That sparked a question on me: is any layer of atmosphere radiating infrared beams themselves? However, it should be noted that I noticed a light pillar in Southwest. So could it be possible that there were ice crystals in the sky at the altitude what corresponded to air temperatures in -30's?

Apologizes for poor English.