**Appendix A**

The heat conduction equation was solved in Matlab using the Partial Di fferential Equation Toolbox. The parabolic heat equation solver uses the Method of Lines, wherein the spatial domain is discretized on a mesh and the partial di fferential equation is converted into a set of ordinary di fferential equations. Boundary conditions were a surface temperature of 0 ◦C, a basal heat flux of 0.04 <sup>W</sup>/m2, a model depth of 25 km and width of 1000 m, insulated right and left boundary conditions, and a sheet thickness of 50 m. Sheets were added at time intervals specified by the accretion rate, at 5 or 10 km depth, and latent heat was accounted for by adding 200 ◦C to the nominal magma temperature (1000 ◦C, appropriate for magma of intermediate composition). Downward displacement of rocks under the injection site was not accounted for. Thermal conductivity in the layer above the injection site was multiplied by *Nu*.
