Whereas there is a significant relationship between overall sea-surface temperature (SST) and tropical cyclone intensity, the relationship is much less clear in the upper range of SST normally associated with these storms. There, we find a step-like, rather than a continuous, influence of SST on cyclone strength, suggesting that there exists a SST threshold that must be exceeded before tropical cyclones develop into major hurricanes. Further, we show that the SST influence varies markedly over time, thereby indicating that other aspects of the tropical environment are also critically important for tropical cyclone intensification. These findings highlight the complex nature of hurricane development and weaken the notion of a simple cause-and-effect relationship between rising SST and stronger Atlantic hurricanes.