There is substantial interest in pseudotachylytes (PT) as products of frictional melting because their study can provide information on the physical and chemical conditions at the earthquake source, including temperature, redox state, stress levels, the role of fluids in fault zone rheology, and the energy budget during seismic slip. PT are dark rocks found in fault zones, that typically contain two components: (a) a very fine grained matrix of recrystallized molten rock showing various flow, shear and chill structures; and (b) embedded clastic material that are products of frictional wear and comminution of the host rock. Frictional melting is thought to initiate between opposing asperity tips during fault slip. While several studies have modeled the macroscopic generation of wear material as well as frictional melts in fault zones, few studies have modeled the microscopic mechanisms of frictional melting at the asperity scale. This study examines the influence of asperity scale fault dynamics on the generation of frictional melts. Our model considers elastic, homogenous and isotropic hemispherical asperities, having a fractal size distribution that scales with slip displacement. Temperature dependence of fault properties is considered. Slip is modeled as adiabatic, and the problem reduced to pure 2-D conduction within a hemisphere. The non-linear PDE is first linearized using the Newton-Kantorovich procedure, and the linearized equation is solved using the delta form of Douglas & Gunn two level scheme. The goals here are to determine: (i) temperature distribution inside a hemispherical asperity, (ii) dependence of temperature on (a) asperity size, (b) asperity spacing and (c) fault zone characteristics (slip velocity, stress, and displacement), (iii) estimate the depth of formation of frictional melt using an appropriate pseudotachylyte geothermometer, and (iv) estimate the critical clast size as a function of fault slip parameters.