We summarize petrological and seismic constraints on the temperature of arc lower crust and shallow mantle, and show that published thermal models are inconsistent with these constraints. We then present thermal models incorporating temperature-dependent viscosity, using widely accepted values for activation energy and asthenospheric viscosity. These produce thin thermal boundary layers in the wedge corner, and an overall thermal structure that is consistent with other temperature constraints. Some of these models predict partial melting of subducted sediment and/or basalt, even though we did not incorporate the effect of shear heating We obtain these results for subduction of 50 Myr old oceanic crust at 60 km/Myr, and even for subduction of 80 Myr old crust at 80 km/Myr, suggesting that melting of subducted crust may not be not restricted to slow subduction of young oceanic crust.