Atmospheric waves have been discovered for the first time in Saturn's neutral upper atmosphere (thermosphere). Waves may be generated from instabilities, convective storms or other atmospheric phenomena. The inferred wave amplitudes change little with height within the sampled region, raising the possibility of the waves being damped, which in turn may enhance the eddy friction within the thermosphere. Using our Saturn Thermosphere Ionosphere General Circulation Model, we explore the parameter space of how an enhanced Rayleigh drag in different latitude regimes would affect the global circulation pattern within the thermosphere and, in turn, its global thermal structure. We find that Rayleigh drag of sufficient magnitude at midlatitudes may reduce the otherwise dominant Coriolis forces and enhance equatorward winds to transport energy from poles toward the equator, raising the temperatures there to observed values. Without this Rayleigh drag, energy supplied into the polar upper atmosphere by magnetosphere-atmosphere coupling processes remains trapped at high latitudes and causes low-latitude thermosphere temperatures to remain well below the observed levels. Our simulations thus suggest that giant planet upper atmosphere global circulation models need to include additional Rayleigh drag in order to capture the effects of physical processes otherwise not resolved by the codes.