The noise temperature of an antenna is a property of the surroundings it is placed in. The term "temperature" is used because a major source of noise in radio communications is thermal energy - which can force electron conduction within a circuit that can drown out weak radio signals (this type of noise is also known as Johnson-Nyquist noise). Note that this noise can occur due to thermal agitation at any part of the system, whether it be the antenna or the PCB traces leading up to the transceiver.

The noise temperature of a system in Kelvin can be related to the strength of the noise over a given bandwidth through the equation below:

$$ \frac{P_N}{B}=k_BT_N $$

where $P_N$ is the noise power in watts, $B$ is the bandwidth in hertz, $k_B$ is the Boltzmann constant, and $T_N$ is the system noise temperature.

The system noise temperature for an antenna is not simply the temperature of the surrounding environment. It also depends on the antenna's radiation pattern - coverage areas with greater gain will clearly receive a greater amount of noise. As such, pointing the antenna towards a heated environment, such as the sun, would result in a higher noise temperature in comparison to pointing at a random patch of sky.

The system noise temperature for an antenna can be calculated with the following equation:

$$ T_N=\frac{1}{4\pi}\int_{0}^{2\pi}\int_{0}^{\pi}F(\theta, \phi)T(\theta, \phi)sin\theta d\theta d\phi $$

where $T(\theta,\phi)$ is the temperature gradient of the surroundings (the temperature for a given spherical coordinate), and $F(\theta,\phi)$ is the radiation pattern of the antenna (this is essentially a weighted average of the temperature).