  The temperature dependence of the generation linewidth for an auto-oscillator
with a nonlinear frequency shift is calculated. It is shown that the frequency
nonlinearity creates a finite correlation time, tau, for the phase
fluctuations. In the low-temperature limit in which the spectral linewidth is
smaller than 1/tau, the line shape is approximately Lorentzian and the
linewidth is linear in temperature. In the opposite high-temperature limit in
which the linewidth is larger than 1/tau, the nonlinearity leads to an apparent
"inhomogeneous broadening" of the line, which becomes Gaussian in shape and has
a square-root dependence on temperature. The results are illustrated for the
spin-torque nano-oscillator.
