In this article we focus our attention on the finite element error analysis for a problem involving both conductive and radiative heat transfer. We sketch the main steps of the analysis by stating the required a priori estimates and the final estimates. The proof for the estimate of the error due to approximation of the geometry is also presented. We prove an abstract estimate for the discretization error in a polygonal domain and combine it to the geometric estimate to yield the final error estimate. A concrete inverse monotone numerical method using view factors is analyzed using the abstract estimates.