The time period around the Noachian-Hesperian boundary, 3.7 million years ago, was an epoch when great geodynamical and environmental changes occurred on Mars. Currently available remote sensing data are crucial for understanding the Martian heat loss pattern and global thermal state in this transitional period. We here derive surface heat flows in specific locations based on estimations of the depth of five large thrust faults, in order to constrain both surface and mantle heat flows. Then, we use heat-producing elements (HPEs) abundances mapped from orbital measurements by the Gamma-Ray Spectrometer (GRS) onboard Mars Odyssey 2001 spacecraft, and geographical crustal thickness variations, to perform a global model for the surface heat flow. The heat loss contribution of large mantle plume beneath the Tharsis and Elysium magmatic provinces is also considered for our final model. We thus obtain a map of the heat flow variation across the Martian surface at the Noachian/Hesperian boundary. Our model also predicts an average heat flow between 32 and 50 mW m−2, which implies that the heat loss of Mars at that time was lower than the total radioactive heat production of the planet, which has profound implications for the thermal history of Mars.