It happens that when an astronomical source, whose angular extent fills
exactly the main lobe, emits as a black-body in the Rayleigh-Jeans regime
, the main-beam temperature is directly the
physical temperature of the emitting source. However, this interpretation
is only valid when the stated conditions are met. This almost never happens
in (sub)-millimeter radio-astronomy because the emitting sources are often
out of local thermodynamic equilibrium and
. So
this interpretation is mostly misleading for newcomers.
As the measured spectral power in radio-astronomy have very small values,
it is easier to express them in term of temperatures that will be orders of
magnitude larger because
. As a matter of fact, most observed brightness
temperatures have values close to 1 (within a factor 1000!)
So it's easier to interpret the above relationship as: expressing spectral powers in terms of temperature is just a useful convenience.