We study the source coding problem in sensor networks deployed to monitor the evolution of spatio-temporal temperature distributions. The sensors sample the temperature field, quantize the samples and transmit the encoded samples through digital channels to some central unit, which computes an estimate of the original temperature field. Our analysis is based on the heat kernel's spectral properties, which are induced by the physics of heat diffusion. We determine rate distortion functions for various source coding schemes. In particular, we compare centralized coding, independent coding, Berger-Tung coding, and predictive quantization.