Characterizing the vigor of magmatic activity in Yellowstone requires knowledge of the mechanisms and rates of heat transport between magma and the ground surface. We present results from a heat flow study in two vapor dominated, acid-sulfate thermal areas in the Yellowstone Caldera, the 0.11 km² Obsidian Pool Thermal Area (OPTA) and the 0.25 km² Solfatara Plateau Thermal Area (SPTA). Conductive heat flux through a low permeability layer capping large vapor reservoirs is calculated from soil temperature measurements at >600 locations and from laboratory measurements of soil properties. The conductive heat output is 3.6 ± 0.4 MW and 7.5 ± 0.4 MW from the OPTA and the SPTA, respectively. The advective heat output from soils is 1.3 ± 0.3 MW and 1.2 ± 0.3 MW from the OPTA and the SPTA, respectively and the heat output from thermal pools in the OPTA is 6.8 ± 1.4 MW. These estimates result in a total heat output of 11.8 ± 1.4 MW and 8.8 ± 0.4 MW from OPTA and SPTA, respectively. Focused zones of high heat flux in both thermal areas are roughly aligned with regional faults suggesting that faults in both areas serve as conduits for the rising acid vapor. Extrapolation of the average heat flux from the OPTA (103 ± 2 W·m⁻²) and SPTA (35 ± 3 W·m⁻²) to the ~35 km² of vapor dominated areas in Yellowstone yields 3.6 and 1.2 GW, respectively, which is less than the total heat output transported by steam from the Yellowstone Caldera as estimated by the chloride inventory method (4.0 to 8.0 GW).