  From the uniformization theorem, we know that every Riemann surface has a
simply-connected covering space. Moreover, there are only three
simply-connected Riemann surfaces: the sphere, the Euclidean plane, and the
hyperbolic plane. In this paper, we collect the known heat kernels, or Green's
functions, for these three surfaces, and we derive the differential forms heat
kernels as well. Then we give a method for using the heat kernels on the
universal cover to generate the heat kernel on the underlying surface.
