To understand role of fluid on earthquake rupture processes, we investigated effects of thermal pressurization on spatial variation of dynamic rupture by computing spontaneous rupture propagation on a rectangular fault. We found thermal pressurization can cause heterogeneity of rupture even on a fault of uniform properties. On drained faults, tractions drop linearly with increasing slip in the same way everywhere. However, by changing the drained condition to an undrained conditionone, the slip-weakening curves become non-linear and depend on locations on faults with small shear zone thickness w, and the dynamic frictional stresses vary spatially and temporally. Consequently, the super-shear transition fault length decreases for small w, and the final slip distribution can have some peaks regardless of w, especially on undrained faults. These effects should be taken into account s forof determining dynamic rupture parameters and modeling earthquake cycles when the presence of fluid is suggested in the source regions.