The effect of the temperature and initial hydrostatic stress has been shown on the propagation of Rayleigh waves in a viscoelastic half-space. It has been explained how the velocity of Rayleigh waves depends not only on the parameters pertaining to the viscoelastic properties of the half-space, but on the temperature and the initial hydrostatic stress of the half-space also. The variations of the phase velocity of Rayleigh waves in dimensionless form with respect to the magnitude of the initial hydrostatic stress under certain practical assumptions have been depicted in graphs after numerical computations. If the temperature and the initial hydrostatic stress of the half-space are neglected, the results obtained are in perfect agreement with the classical case as obtained by Caloi for the propagation of Rayleigh waves in a viscoelastic medium.