  A nanomechanical resonator coupled to a tunnel junction is studied. The
oscillator modulates the transmission of the junction, changing the current and
the noise spectrum. The influence of the oscillator on the noise spectrum of
the junction is investigated, and the noise spectrum is obtained for arbitrary
frequencies, temperatures and bias voltages. We find that the noise spectrum
consists of a noise floor and a peaked structure with peaks at zero frequency,
the oscillator frequency and twice the oscillator frequency. The influence of
the oscillator vanishes if the bias voltage of the junction is lower than the
oscillator frequency. We demonstrate that the peak at the oscillator frequency
can be used to determine the oscillator occupation number, showing that the
current noise in the junction functions as a thermometer for the oscillator.
