The density-density dynamical correlation function of a simple fluid in a finite container subject to a constant temperature difference is explicitly obtained. In small systems, such as those realized in computer experiments, new peaks appear in the scattering spectrum, even at equilibrium, arising from standing waves produced by the fluctuations. Away from equilibrium, these peaks are asymmetric in the same manner as the Brillouin lines. The macroscopic limit is also considered and the correction to the usual “infinite system approximation” is explicitly obtained.