Thermal radiation from a fully ionized gas near the plasma frequency is investigated theoretically with consideration given to boundary effects. It is shown that the emission spectrum is a relatively complicated function of frequency, temperature, density, and geometry, but that the absorption spectrum can be approximated by a simple function of the three parameters representing frequency, collisions, and geometry. The sensitivity of the absorption curve to these parameters is investigated, and the results are used to interpret recently measured infrared radiation from a theta pinch.