A transient three-dimensional heat transfer model is developed for a 3 kWth solar thermochemical reactor for H2O and CO2 splitting via two-step nonstoichiometric ceria cycling. The reactor consists of a windowed solar receiver cavity, counter-rotating reactive and inert cylinders, and insulated reactor walls. The counter-rotating cylinders allow for continuous fuel production and heat recovery. The model is developed to solve energy conservation equations accounting for conduction, convection, and radiation heat transfer modes, and chemical reactions. Radiative heat transfer is analyzed using a combination of the Monte Carlo ray-tracing method, the net radiation method, and the Rosseland diffusion approximation. Steady-state temperatures, heat fluxes, and nonstoichiometry are reported. A temperature swing of up to 401 K, heat recovery effectiveness of up to 95%, and solar-to-fuel efficiency of up to 5% are predicted in parametric studies.