I just got myself an infrared thermometer. I wouldn't have been able to predict what temperature it would give me when pointing at the sky, but it turned out to be -2 °C the first time I measured, and slightly going up and down with the temperature on the ground (say from -6 °C to 2 °C in the course of a day in which the ground temperature goes from 20 °C at night to 30 °C during daytime).
Some details: this was for pointing straight up (as long as its not pointing too closely to the sun), a clear sky and a humidity of 63% according to internet. The range in which it measures radiation is from 8-14 μm and the specified range of temperatures is -50 to 550 °C.
What is it that causes this reading?
Answer
You are likety to be directly measuring the greenhouse effect of the atmosphere. The fact that your cursory measurements seem to be correlated with the air temperature around you supports this idea: the measurement is higher in the day because the Earth itself is hotter and radiating back into space more powerfully. Greenhouse gasses are thus absorbing some of this radiation, and sending their re-radiated infrared back to your thermometer. The thermometer will also be influenced by clouds and the like, even mist and haze that may be hard to discern as clouds.
I would try noting the thermometer's reading with different atmospheric conditions, noting the sky condition (cloudy, clear), local temperature and humidity. Although I wouldn't be too surprised if the reading were not influenced by the last: humidity at the ground may not give a reliable idea of how much water there is in the various jetstreams and so forth at different heights.
But you're definitely measuring something "real" and repeatable: see the following experiment, which is a formalisation of what you have done, suggested by NASA:
http://mynasadata.larc.nasa.gov/804-2/1035-2
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