Does an increase in temperature affect the intensity of a tropical cyclone?

One of the necessary ingredients for tropical storm development is a surface temperature equal to or greater than 28 C. The result is a high evaporative loss of water as the wind spirals inward and upward into the developing storm. This evaporation is necessary for the release of the heat of condensation in the upper levels of the storm which acts to lower the pressure. While absolutely necessary for helping to generate and sustain the storm it is not yet fully understood what the effect would be to increase that surface temperature by another degree or so in the areas where the storms form. At higher latitudes warmer surface temps would mean that storms would maintain their strength longer than they do now. We know this and we see it for example in the Gulf of Mexico where storms weakened by having ped over Cuba or south Florida or the Yucatan gather renewed strength over the warmer Gulf waters. The question in my mind is the degree of intensification. I believe more research is still required in this area.