  Magmatism in subduction zones builds continental crust and causes most of
Earth's subaerial volcanism. The production rate and composition of magmas are
controlled by the thermal structure of subduction zones. A range of geochemical
and heat flow evidence has recently converged to indicate that subduction zones
are hotter at lithospheric depths beneath the arc than predicted by canonical
thermomechanical models, which neglect magmatism. We show that this discrepancy
can be resolved by consideration of the heat transported by magma. In our one-
and two-dimensional numerical models and scaling analysis, magmatic transport
of sensible and latent heat locally alters the thermal structure of canonical
models by $\sim$300 K, increasing predicted surface heat flow and
mid-lithospheric temperatures to observed values. We find the advection of
sensible heat to be larger than the deposition of latent heat. Based on these
results we conclude that thermal transport by magma migration affects the
chemistry and the location of arc volcanoes.
