Integral methods have been applied to the prediction of the far field thermal impact of a nuclear waste repository. The heat balance integral (HBI) has been applied to a semi-infinite layered domain in which the repository is represented by an infinite plane beneath either one or two sublayers. Calculations for pressurized water reactor spent fuel with an initial thermal loading of 60 kW/acre are carried out for various stratigraphies and overburden compositions. Thermophysical properties of all geologic media are assumed independent of temperature, but thermal conductivities are varied to include upper and lower bounds, as well as generic values. The results demonstrate that thermophysical properties of the overburden have the most important influence on temperature distributions and peak temperature at any position above the repository. Where a comparison to exact or numerical solutions is possible, the HBI predicts maximum temperature increases in the overburden to within 10%. Heat fluxes to the earth’s surface are found to be relatively insensitive to overburden composition. For dome salt, the surface heat flux is 1.2 to 2.7% of the initial thermal loading over 105 yr. This variation corresponds to about a threefold variation in the effective thermal conductivity of the overburden. Similarly, low percentages of thermal loading reach the surface for bedded salt, granite, basalt, or shale. In any case, the present results provide upper bound estimates on both repository temperature and surface heat flux.