A linearized stability analysis has been applied to a fluid flowing in a gravity field between horizontal planes in Couette flow under conditions such that the temperature of the bottom plane exceeds that of the top. The analysis was carried out for two different forms of constitutive equations: (1) a “generalized second‐order equation,” which is a differential model usually associated with continuum theories, and (2) an integral equation which has its basis in a molecular model and accounts for network junctions which rupture at a certain critical strain. Both models lead, after application of a number of simplifying assumptions, to the same set of differential equations which must be satisfied at a condition of nonoscillatory marginal stability. In contrast to the case for Newtonian fluids, there is coupling between the equations describing momentum and energy disturbances. This fact leads, for viscoelastic fluids, to a critical Rayleigh number which is dependent upon flow properties. In particular, the critical Rayleigh number is highly sensitive to the sign and magnitude of the second normal stress difference, a result shared with earlier studies of some other stability problems. Significance of the results is discussed.