On interannual time scales, tropical mean precipitation anomalies P' appear quite scattered in relation to tropical average sea surface temperature (SST) anomalies Ts', based on examination of a number of observational datasets and of atmospheric general circulation model (GCM) results. Even though SST is locally important for determining precipitation, for a given warm SST anomaly, the tropical average precipitation anomalies can be of either sign due to the near-cancellation of positive against negative values. No simple relation is found between P' and Ts'. On the other hand, tropical average tropospheric temperature anomalies T' are approximately linearly related to SST forcing. The scatter of P' versus Ts' and T' challenges the prevailing view that tropical tropospheric temperature anomalies are proportional to tropical convective heating anomalies(i.e. precipitation anomalies), while the latter are governed by SST forcing. A simple analytical model shows that convective heating anomalies are more strongly influenced by dry static energy transports into or out of the tropics and by nonlinearities within the tropics than are the tropospheric temperature anomalies. As convection maintains a quasi-balance between surface and tropospheric temperature, the tropical average convective heating (i.e., precipitation) anomalies react to oppose any processes that would tend to cool the tropical troposphere. On interannual time scales, the integral constraint on tropical average precipitation is dominated by the dry static energy transport into or out of the tropics. Thus while tropical average tropospheric temperature is closely related to SST, tropical-midlatitude transports can create large scatter in tropical average precipitation.