The nonlocat specific heat is calculated for the two-dimensional Ising model and found to be identical to that found by Bray for the four-dimensional model. Furthermore, it is noted that analytic continuation in terms of a spectral function provides an especially simple description of the nonlocal specific heat. From unitarity the spectral function is the rate of pair production in the Minkowski metric, and is calculated to be equal to the velocity of the outgoing particles.