  We study a granular gas heated by a stochastic thermostat in the dilute
limit. Starting from the kinetic equations governing the evolution of the
correlation functions, a Boltzmann-Langevin equation is constructed. The
spectrum of the corresponding linearized Boltzmann-Fokker-Planck operator is
analyzed, and the equation for the fluctuating transverse velocity is derived
in the hydrodynamic limit. The noise term (Langevin force) is thus known
microscopically and contains two terms: one coming from the thermostat and the
other from the fluctuating pressure tensor. At variance with the free cooling
situation, the noise is found to be white and its amplitude is evaluated.
