Thermal perturbations associated with seismic slip on faults may significantly affect the dynamic friction and the mechanical energy release during earthquakes. This paper investigates details of the coseismic temperature increases associated with the elastodynamic propagation of shear cracks and effects of fault heating on the dynamic fault strength. Self-similar solutions are presented for the temperature evolution on a surface of a mode II shear crack and a self-healing pulse rupturing at a constant velocity. The along-crack temperature distribution is controlled by a single parameter, the ratio of the crack thickness to the width of the conductive thermal boundary layer, $bar{w}$. For thick cracks, or at early stages of rupture ($bar{w}$ > 1), the local temperature on the crack surface is directly proportional to the amount of slip. For thin cracks, or at later times ($bar{w}$ < 1), the temperature maximum shifts toward the crack tip. For faults having slip zone thickness of the order of centimeters or less, the onset of thermally induced phenomena (e.g., frictional melting, thermal pressurization, etc.) may occur at any point along the rupture, depending on the degree of slip localization and rupture duration. In the absence of significant increases in the pore fluid pressure, localized fault slip may raise temperature by several hundred degrees, sufficient to cause melting. The onset of frictional melting may give rise to substantial increases in the effective fault strength due to an increase in the effective fault contact area, and high viscosity of silicate melts near solidus. The inferred transient increases in the dynamic friction (viscous braking) are consistent with results of high-speed rock sliding experiments and might explain field observations of the fault wall rip-out structures associated with pseudotachylites. Possible effects of viscous braking on the earthquake rupture dynamics include (1) delocalization of slip and increases in the effective fracture energy, (2) transition from a crack-like to a pulse-like rupture propagation, or (3) ultimate rupture arrest. Assuming that the pulse-like ruptures heal by incipient fusion, the seismologic observations can be used to place a lower bound on the dynamic fault friction. This bound is found to be of the order of several megapascals, essentially independent of the earthquake size. Further experimental and theoretical studies of melt rheology at high strain rates are needed to quantify the effects of melting on the dynamic fault strength.