The thermal boundary layer at the surface of a volcanic lava dome is investigated through a continuum model of the thermodynamic advection diffusion processes resulting from magmatic gas flow through the dome matrix. The magmatic gas mass flux, porosity and permeability of the rock are identified as key parameters. New, theoretical, nonlinear steady-state thermal profiles are reported which give a realistic surface temperature of 210 degC for a region of lava dome surface through which a gas flux of 3.5 x 10-3 kg s-1 m-2 passes. This contrasts favourably with earlier purely diffusive thermal models, which cool too quickly. Results are presented for time-dependent perturbations of the steady states as a response to: changes in surface pressure, a sudden rockfall from the lava dome surface, and a change in the magmatic gas mass flux at depth. Together with a generalized analysis using the method of multiple scales, this identifies two characteristic time scales associated with the thermal evolution of a dome carapace: a short time scale of several minutes, over which the magmatic gas mass flux, density, and pressure change to a new quasi-steady-state, and a longer time scale of several days, over which the thermal profile changes to a new equilibrium distribution. Over the longer time scale the dynamic properties of the dome continue to evolve, but only in slavish response to the ongoing temperature evolution. In the light of this time scale separation, the use of surface temperature measurements to infer changes in the magmatic gas flux for use in volcanic hazard prediction is discussed.