Temperature measurements taken in young, landfast Antarctic sea ice show daily oscillations consistent with heating by solar radiation. We present and solve a heat conduction model for the temperature with a non-linear thermal capacity and a distributed source term for solar power absorption based on Monte Carlo scattering simulations of penetrating photons. We observe two characteristic modes for solar heating in sea ice, one dominated by travelling thermal waves or conduction in the upper half, and the other dominated by in-place solar heating in the lower half. We note that deep thermal responses to solar radiation are larger by a factor of ∼ 10 than predicted by scattering measurements, due possibly to the presence of algae and/or dissolved organic material.