A solution method is described and applied for treating non-similar thermal boundary layers. The solutions are locally autonomous (that is, independent of information from other streamwise locations) and are found by solving quasi-ordinary differential equations of the similarity type. All non-similar terms appearing in the conservation equations are retained without approximation, and only in derived subsidiary equations are terms selectively neglected. The accuracy of the results can be appraised from comparisons internal to the method itself. Thermal boundary-layer non-similarity arising both from velocity-field, non-similarity and from streamwise variations of surface temperature are analyzed. Numerical results for the surface heat transfer and for the boundary-layer temperature distribution are presented for various physical situations.