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The shape of a stationary solid-liquid interface in a temperature gradient near a grain boundary in a pure material is calculated for anisotropic crystal-melt surface tension and equal thermal conductivities of crystal and melt. Results are compared with those for the well-known problem of the two-dimensional equilibrium shape of a crystal. For small anisotropy, the resulting interface shapes have continuously turning tangents but differ in detail from the grain boundary groove shapes that have been calculated for isotropic surface tension. For larger anisotropy, the interface shapes have discontinuities in slope as a result of missing orientations; these missing orientations are the same as those that would be missing on the corresponding equilibrium interface shape. In cases where a normal to the grain boundary or to the macroscopic interface is in the range of missing orientations on the corresponding equilibrium shape, the groove shape may contain some of these orientations as well as having varifold surfaces. Detailed numerical results are presented for a surface tension with fourfold symmetry.