We have performed a theoretical study of temperatures beneath the surface of a comet's nucleus. We solve the one-dimensional heat conduction equation for the outer portion of the comet. The upper boundary condition of the model is given by energy balance at the surface of the nucleus, including conduction of heat inward, radiation, insolation as modified by the coma, and sublimation. Our coma model assumes single scattering and includes attenuation of direct sunlight by dust grains, scattering of light onto the nucleus, and infrared radiation by dust grains. The lower boundary condition is zero net heat flux around an orbit. The thermal conductivity expression for the nucleus includes direct conduction at grain boundaries, radiative conduction, and Knudsen flow vapor diffusion. The thermal diffusivity of the nucleus and the resultant temperature profiles are shown to be strongly dependent on the physical properties of the material, including porosity, pore size, and compaction. The temperature profiles and the equilibrium temperature deep within the comet also depend on the functional relationship between thermal conductivity and temperature; the highest deep equilibrium temperatures are found for models where the thermal conductivity increases strongly with increasing temperature. The dependence of temperatures on the albedo and thermal emissivity of the nucleus is also calculated, as well as the variation of temperature with latitude for a variety of pole orientations. The effect of a dust mantle on subsurface temperatures is also investigated. All calculations are presented for short-period comets with orbits that make them accessible for exploration by spacecraft rendezvous. In situ measurements of the thermal profile in the upper meter of a comet nucleus can substantially constrain the thermal diffusivity of the material, which in turn can provide significant information about the physical properties of the nucleus.