The Q-state Monte Carlo, Potts model is used to investigate 2D, anisotropic, grain growth of single-phase materials subject to temperature gradients. Anisotropy is simulated via the use of nonuniform grain boundary surface energies, and thermal gradients are simulated through the use of variable grain boundary mobilities. Hexagonal grain elements are employed, and elliptical Wulff plots are used to assign surface energies to grain lattices. The mobility is set to vary in accordance with solutions to a generalized heat equation and is solved for two separate values of the mobility coefficient. Among other findings, the results reveal that like isotropic grain growth, under the influence of a thermal gradient, anisotropic grain growth also demonstrates locally normal growth kinetics.