Are warming sea temperatures making hurricanes worse?

One sees constant discussion about whether global warming is making hurricanes worse. There is a lot of rain with hurricanes, which means huge energy comes from the ocean. It takes about 2400 kJ to evaporate a kg (about a litre) of water and rain means there must have been evaporation in the first place. The energy for the evaporation comes almost entirely from the water, because air has such a small heat capacity that if the energy came from the air it would quickly be cooled. Air has a volumetric heat capacity of about 1.2 kJ per cubic metre for every 1 deg C drop in temperature. Water has a volumetric heat capacity of about 4180 kJ per cubic metre for every 1 deg C drop in temperature. 
http://www.aoml.noaa.gov/hrd/tcfaq/D7.html  tells us that a hurricane has about 5.2x10¹⁹ J or 5.2x10¹⁶ kJ of energy per day spread out over about an area with radius 665 km. My calculations give that this is about 37429 kJ per square metre per day or 10.4 kWh per square metre per day. By comparison one may get about 8 kWh per day per square metre from the sun (Weatherspark will tell you how much for you area). If the energy is coming from the water, then one cubic metre of water (1000 kg) would be cooled 37429/(4180)=9 deg C in a day. So if we do not have deep hot water to provide the energy, the hurricane will lose strength. It seems obvious that warming sea temperatures will fuel hurricanes more, or have I missed something?