The strongest hurricanes are getting stronger as the oceans heat up especially over the North Atlantic. Sensitivity of hurricane intensity to ocean heating is an important variable for understanding what hurricanes might be like in the future, but reliable estimates are not possible with short time-series records. Studies using paired values of intensity and sea-surface temperature (SST) are also limited because most pairs represent hurricanes in an environment that is less than thermodynamically optimal. Here we overcome these limitations using spatial grids and estimate the sensitivity to be 8.2 +/- 1.19 m/s/C (s.e.) for hurricanes over seas hotter than 25C across the North Atlantic. We find that the sensitivity is significantly lower in a high-resolution general circulation model. Results indicate a greater likelihood of more powerful hurricanes during the 21st century as oceans continue to warm over this part of the world, but call into question the usefulness of current GCMs for helping us understand what might happen in the future.