A theory for approximately steady thermal degradation of solids is developed from a superset of nonlinear integral-differential equations. The theory extends previous work, using a degradation model that is more consistent than previously published models and fully accounts for surface radiation losses. The thermal decomposition of the solid is assumed to follow a single-step first-order Arrhenius reaction. A quasi-steady regime is identified and approximate solutions are compared with experimental results for PMMA and numerical results obtained by integrating the full model. The numerical solutions are found to compare well with experimental results and the approximate solutions compare well with the numerics. Furthermore, it is found that the quasi-steady mass loss rate gives a good estimate of the average mass loss rate even during thermally thin degradation. To simplify interpretation and to aid the analysis, the degradation kinetics are re-cast in terms of a critical temperature and a critical temperature range. Application of the theory to practical situations and other modelling approaches is also discussed.