Empirical relationships between tropical sea surface temperature (SST) and atmospheric deep convection are examined. Large-scale features of tropical deep convection are estimated from two independent satellite datasets: monthly mean outgoing longwave radiation of 15 years and high-resolution pentad (5 day) fractional coverage of infrared radiation histograms of 5 years. Results based on the two datasets lead to the same conclusions. The relationships are addressed from two aspects: how deep convection varies with changing SST and how it varies at constant SST. Deep convection remains weak and rarely observed for SST < 26-degrees-C; the frequency and mean intensity of deep convection substantially increase with SST from 26-degrees-C up to about 29.5-degrees-30-degrees-C, and then decay for.further increasing SST. Meanwhile, in the warm pool region with SST > 27-degrees-C, situations of no deep convection and vigorous deep convection can both be observed; the areal coverage of convectively related high clouds is always dominated by that of clear sky and low clouds. The variability of deep convection, thus becomes larger for higher SST. The large variability of deep convection at constant high SST is found to be attributable to the differences in mean spatial distributions and in the annual variations of SST and deep convection. The annual variations in areal coverages by warm sea surfaces and active deep convection are out of phase in the Indian and western Pacific oceans. The tendency of an increase in deep convection with SST is more identifiable in January but less clear in April. In general, the relationship is less apparent for the in convergence zone than the other regions of the tropical oceans. Therefore, neither the increase in deep convection with SST nor the large variability of deep convection at constant high SST is generally representative of the relationship between the two fields in the tropics. The empirical relationship varies in space and time. It is argued that, in the warm pool region, the absence of deep convection at particular locations and times and the large variability of deep convection do not imply changes in high SST have little effect on deep convection. Rather, they reflect that other factors can sometimes be dominantly unfavorable to deep convection. The influence of SST on deep convection in the warm pool region is revealed by the fact that, as SST increases, deep convection becomes more frequent and, when it occurs, tends to be more intense on average, regardless of other factors. This increase in deep convection with SST is found to be smooth and continuous with no abrupt change at any particular SST.