  We report the measurement of the fluctuations of a transmon qubit through the
noise spectrum of the microwave signal that measures its state. The amplitude
of the Lorentzian noise power spectrum allows to determine the average qubit
excitation, in agreement with the estimated thermal radiation reaching the
sample. Its width yields the qubit energy relaxation rate which decreases with
temperature, contrary to the predictions for a two-level system solely coupled
to thermal radiation. This indicates the existence of another non-radiative
energy relaxation channel for the qubit.
