Forecasting destructive hurricane potential is complicated by substantial, unexplained intraannual variation in storm-specific power dissipation index (PDI, or integrated third power of wind speed), and interannual variation in annual accumulated PDI (APDI). A growing controversy concerns the recent hypothesis that the clearly positive trend in North Atlantic Ocean (NAO) sea surface temperature (SST) since 1970 explains increased hurricane intensities over this period, and so implies ominous PDI and APDI growth as global warming continues. To test this “SST hypothesis” and examine its quantitative implications, a combination of statistical and probabilistic methods were applied to National Hurricane Center HURDAT best-track data on NAO hurricanes during 1880–2002, and corresponding National Oceanographic and Atmospheric Administration Extended Reconstruction SST estimates. Notably, hurricane behavior was compared to corresponding hurricane-specific (i.e., spatiotemporally linked) SST; previous similar comparisons considered only SST averaged over large NAO regions. Contrary to the SST hypothesis, SST was found to vary in a monthly pattern inconsistent with that of corresponding PDI, and to be at best weakly associated with PDI or APDI despite strong correlation with corresponding mean latitude (R2= 0.55) or with combined mean location and a ∼90-year periodic trend (R2= 0.70). Over the last century, the lower 75% of APDIs appear randomly sampled from a nearly uniform distribution, and the upper 25% of APDIs from a nearly lognormal distribution. From the latter distribution, a baseline (SST-independent) stochastic model was derived predicting that over the next half century, APDI will not likely exceed its maximum value over the last half century by more than a factor of 1.5. This factor increased to 2 using a baseline model modified to assume SST-dependence conditioned on an upper bound of the increasing NAO SST trend observed since 1970. An additional model was developed that predicts PDI statistics conditional on APDI. These PDI and APDI models can be used to estimate upper bounds on indices of hurricane power likely to be realized over the next century, under divergent assumptions regarding SST influence.