A theory is described based on resonant thermal diffusion waves in the sun that explains many details of the paleotemperature record for the last 5.3 million years. These include the observed periodicities, the relative strengths of each observed cycle, and the sudden emergence in time for the 100 thousand year cycle. Other prior work suggesting a link between terrestrial paleoclimate and solar luminosity variations has not provided any specific mechanism. The particular mechanism described here has been demonstrated empirically, although not previously invoked in the solar context. The theory, while not without its own unresolved issues, also lacks most of the problems associated with Milankovitch cycle theory.