Martian thermal state and evolution depend principally on the radiogenic heat-producing element (HPE) distributions in the planet's crust and mantle. The Gamma-Ray Spectrometer (GRS) on the 2001 Mars Odyssey spacecraft has mapped the surface abundances of HPEs across Mars. From these data, we produce the first models of global and regional surface heat production and crustal heat flow. As previous studies have suggested that the crust is a repository for approximately 50% of the radiogenic elements on Mars, these models provide important, directly measurable constraints on Martian heat generation. Our calculations show considerable geographic and temporal variations in crustal heat flow, and demonstrate the existence of anomalous heat flow provinces. We calculate a present day average surface heat production of 4.9 ± 0.3 × 10−11 W · kg−1. We also calculate the average crustal component of heat flow of 6.4 ± 0.4 mW · m−2. The crustal component of radiogenically produced heat flow ranges from <1 mW · m−2 in the Hellas Basin and Utopia Planitia regions to ∼13 mW · m−2 in the Sirenum Fossae region. These heat production and crustal heat flow values from geochemical measurements support previous heat flow estimates produced by different methodologies.