Fuzzballs and black hole thermodynamics

The fuzzball construction resolves the black hole information paradox by making spacetime end just before the horizon is reached. But if there is no traditional horizon, then do we lose the elegant relations of black hole thermodynamics? Using an argument similar to modular invariance, we argue that the answer is no; the completeness of fuzzball states implies that the generic fuzzball indeed reproduces the thermal properties attributed to the traditional hole.