A one-dimensional (1-D) analytic solution is developed for heat transport through an aquifer system where the vertical temperature profile in the aquifer is nearly uniform. The general anisotropic form of the viscous heat generation term is developed for use in groundwater flow simulations. The 1-D solution is extended to more complex geometries by solving the equation for piece-wise linear or uniform properties and boundary conditions. A moderately complex example, the Eastern Snake River Plain (ESRP), is analyzed to demonstrate the use of the analytic solution for identifying important physical processes. For example, it is shown that viscous heating is variably important and that heat conduction to the land surface is a primary control on the distribution of aquifer and spring temperatures. Use of published values for all aquifer and thermal properties results in a reasonable match between simulated and measured groundwater temperatures over most of the 300 km length of the ESRP, except for geothermal heat flow into the base of the aquifer within 20 km of the Yellowstone hotspot. Previous basal heat flow measurements (∼110 mW/m²) made beneath the ESRP aquifer were collected at distances of >50 km from the Yellowstone Plateau, but a higher basal heat flow of 150 mW/m² is required to match groundwater temperatures near the Plateau. The ESRP example demonstrates how the new tool can be used during preliminary analysis of a groundwater system, allowing efficient identification of the important physical processes that must be represented during more-complex 2-D and 3-D simulations of combined groundwater and heat flow.