Abundant observations of seismic anisotropy in subduction zones attest that the material in the mantle wedge has a strong fabric and therefore should be mechanically anisotropic. In this paper, we examine the effect of anisotropic viscosity on the thermal structure of subduction zone mantle wedges and quantify its importance relative to other thermal and rheological factors. Using two‐dimensional finite element kinematic models we find that anisotropic viscosity results in two substantial changes: a hotter slab‐wedge interface and time variability of the melt production rate and excess temperatures. Although not as significant as the effect of temperature‐dependent viscosity, anisotropy leads to an increase of up to 35°C in the temperature along the slab‐wedge interface. A hotter slab‐wedge interface can change the depth extent of the seismogenic zone, limit the depth to which hydrous minerals can carry water, and influence flux melting. Time variability of the thermal field is a novel result of adding anisotropic viscosity to our models. This time variability results from heterogeneity in material alignment and could explain temporal changes in subduction zone magmatism without invoking a change in the wedge geometry, slab age, or composition.