The temperature of SiO2 in high-pressure shock states has been measured for samples of single-crystal α-quartz and fused quartz. Pressures between 60 and 140 GPa have been studied using projectile impact and optical pyrometry techniques at Lawrence Livermore National Laboratory. Both data sets indicate the occurrence of a shock-induced phase transformation at ~70 and ~50 GPa along the α- and fused quartz Hugoniots, respectively. The suggested identification of this transformation is the melting of shock-synthesized stishovite, with the onset of melting delayed by metastable superheating of the crystalline phase. Some evidence for this transition in conventional shock wave equation of state data is given, and when these data are combined with the shock temperature data, it is possible to construct the stishovite-liquid phase boundaries. The melting temperature of stishovite near 70 GPa pressure is found to be 4500 K, and melting in this vicinity is accompanied by a relative volume change and latent heat of fusion of ~2.7% and ~2.4 MJ/kg, respectively. The solid stishovite Hugoniot centered on α-quartz is well described by the linear shock velocity-particle velocity relation, us=1.822 up+1.370 km/s, while at pressures above the melting transition, the Hugoniot centered on α-quartz has been fit with us=1.619 up+2.049 km/s up to a pressure of ~200 GPa. The melting temperature of stishovite near 100 GPa suggests an approximate limit of 3500 K for the melting temperature of SiO2-bearing solid mantle mineral assemblages, all of which are believed to contain Si4+ in octahedral coordination with O2-. Thus 3500 K is proposed as an approximate upper limit to the melting point and the actual temperature in the earth's mantle. Moreover, the increase of the melting point of stishovite with pressure at 70 GPa is inferred to be ~11 K/GPa. Using various adiabatic temperature gradients in the earth's mantle and assuming creep is diffusion controlled in the lower mantle, the current results could preclude an increase of viscosity by more than a factor of 103 with depth across the mantle.