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Antenna temperature (or antenna noise temperature) is not the physical temperature of the antenna, but a measure of the noise that competes with the desired signal, possibly obscuring it. Noise is unwanted signal, i.e., in radio astronomy, other than the specific signal from the desired portion of the sky, or in radio-based communications, other than the signal representing the transmitted data. The antenna temperature is a noise temperature, i.e., expressing such noise as a temperature, relating to the power of the noise as:
T = P / (kBB)
Clearly included in antenna temperature is the noise from the antenna itself (there is noise inherent in its own temperature) and often the term antenna temperature is meant to include noise received from the antenna but stemming from other sources that affect the antenna, such as the Earth and the rest of the sky, treating the term as representing "all the noise mixed with the signal received from the antenna", which can include, in addition to the antenna itself:
Antenna noise temperature is specific to both frequency and direction.
Representation of noise as a temperature is useful because of their relation: anything (e.g., circuits, cables) with some heat (i.e., above absolute zero) produces thermal noise which is in proportion to the item's temperature. (Such thermal noise is a reason for cryogenic cooling of some equipment to maximize sensitivity by avoiding covering up the desired signal.) Furthermore, noise temperature is a logarithmic measure of the noise, which allows total noise to be calculated by adding the noise temperatures of each of the devices and cables through which the signal is traveling.
The signal itself can also be expressed as a temperature, which is termed the brightness temperature; being expressed in the same units, this facilitates a kind of signal-versus-noise comparison.