A state-variable constitutive relation that can describe the dependence of friction on temperature at or near steady state conditions is presented. The relation is derived from existing state-variable relations used to describe velocity dependence and the assumption that the micromechanisms of friction are thermally activated and follow an Arrhenius relationship. The relation adequately describes the transient and steady state friction behavior displayed in sliding experiments on 1.5-mm-thick layers of fine-grained (<100 μm diameter) quartz gouge. Gouge layers were sheared up to 10 mm between rough steel surfaces at a constant effective confining pressure of 20 MPa and under room-dry or water-saturated conditions in a servo-controlled triaxial apparatus. In each experiment, velocity was stepped between 4, 0.4, and 0.04 μm/s at constant temperature, and temperature was stepped between 24¿, 57¿, and 82 ¿C at a constant velocity of 0.04 μm/s. Coefficient of friction was calculated from measurements of sample strength using corrections for all apparatus effects including the temperature and velocity dependent strength of the metal sleeves used to isolate the sample and of the graphite-lubricated interface that allowed lateral slip of the sample halves. Experiments indicate that (1) an abrupt increase in temperature induces a transient friction response similar to that induced by a step decrease in velocity, (2) the transient friction response is relatively symmetric for steps up and steps down in temperature, and (3) the characteristic slip distance for friction to evolve to steady state after step changes in temperature is the same as after step changes in velocity. The apparent activation energy determined for wet quartz gouge at the test conditions is 89¿23 kJ/mol. This value is consistent with models of friction involving failure of contact junctions by subcritical crack growth and time dependent strengthening of contact junctions by either increasing the true area of contact through subcritical cracking or by increasing the quality of contact junctions through healing.