The power of singularity of the temperature gradient at a macrocrack tip is analyzed in this work. For a crack in an infinite medium. Williams' method of eigenfunction expansions is extended to heat conduction problems with a crack and comparison with the complex function approach is made. The intensity factor of temperature gradient (IFTG) is introduced to quantify the thermal energy cumulated in the neighborhood of a macrocrack tip. As an entirety, the power of singularity of the temperature gradient is analyzed for a crack in both isotropic and orthotropic media, and an interfacial crack between dissimilar materials. It is shown that the power of singularity of the temperature gradient is not affected by the discontinuous jumps of the thermal properties across the material interface, while that for a crack in an orthotropic medium depends on the ratio of thermal conductivities in the principal directions of material orthotropy.