The assumption that tropical cyclones respond primarily to sea surface temperatures (SSTs) local to their main development regions underlies much of the concern regarding the possible impacts of anthropogenic greenhouse warming on tropical cyclone statistics. Here the observed relationship between changes in sea surface temperature and tropical cyclone intensities in the Atlantic basin is explored. Atlantic tropical cyclone intensity fluctuations and storm numbers are shown to depend not only upon SST anomalies local to the Atlantic main development region, but also in a negative sense upon the tropical mean SST. This behavior is shown in part to be consistent with changes in the tropical cyclone potential intensity that provides an upper bound on storm intensity. However, Atlantic tropical cyclone intensity fluctuations are more nonlocal than the potential intensity itself and specifically vary along with Atlantic main development region SST anomalies relative to the tropical mean SST. This suggests that there is no straightforward link between warmer SSTs in the main development region and more intense tropical cyclones.