  We study Kuramoto phase oscillators with temporal fluctuations in the
frequencies. The infinite-dimensional system can be reduced in a Gaussian
approximation to two first-order differential equations. This yields a solution
for the \emph{time-dependent} order parameter, which characterizes the
synchronization between the oscillators. The known critical coupling strength
is exactly recovered by the Gaussian theory. Extensive numerical experiments
further show that the analytical results are very accurate below and
sufficiently above the critical value. We obtain the asymptotic order parameter
\emph{in closed form}, which suggests a tighter upper bound for the
corresponding scaling. As a last point, we elaborate the Gaussian approximation
in complex networks with distributed degrees.
