Antenna Temperature is a measure of the noise being produced by an antenna in a given environment. This is also called an Antenna Noise Temperature. It is not the physical temperature of the antenna. This temperature depends of the gain, radiation pattern and the noise that the antenna picks up from the surrounding environment.

The Antenna Temperature can be represented by the following formula:

This equation shows that the antenna temperature is calculated by integrating over the entire sphere, based on the radiation pattern of the antenna and the temperature distribution of the antenna.

is the radiation pattern of the antenna. 

is temperature distribution of the antenna based on its surroundings. For example, the temperature of the night sky is 4 Kelvin, the value of the temperature pattern in the direction of the ground would be based on the physical temperature of the ground.