  We develop a model for sheared gouge layers that accounts for the local
increase in temperature at the grain contacts during sliding. We use the shear
transformation zone (STZ) theory, a statistical thermodynamic theory, to
describe irreversible macroscopic plastic deformations due to local
rearrangements of the gouge particles. We track the temperature evolution at
the grain contacts using a one dimensional heat diffusion equation. At low
temperatures, the strength of the asperities is limited by the flow strength,
as predicted by dislocation creep models. At high temperatures, some of the
constituents of the grains may melt leading to the degradation of the asperity
strength. Our model predicts a logarithmic rate dependence of the steady state
shear stress in the quasi-static regime. In the dense flow regime the
frictional strength decreases rapidly with increasing slip rate due to the
effect of thermal softening at the granular interfaces. The transient response
following a step in strain rate includes a direct effect and a following
evolution effect, both of which depend on the magnitude and direction of the
velocity step. In addition to frictional heat, the energy budget includes an
additional energy sink representing the fraction of external work consumed in
increasing local disorder. The model links low-speed and high-speed frictional
response of gouge layers, and provides an essential ingredient for multiscale
modeling of earthquake ruptures with enhanced coseismic weakening.
