The evaluation and applicability of hybrid transfinite-element formulations are described for transient nonlinear thermal models with particular reference to radiation effects. The formulations are developed from basic concepts and evaluated for both one- and two-dimensional thermal models. The methodology presented is a hybrid approach, in that it combines finite elements, classical Galerkin schemes, and transform methods. Basic features of the hybrid formulations and the associated solution scheme are first described. Therein, numerical test models are presented to evaluate the applicability for predicting the nonlinear transient response in one- and two-dimensional thermal models influenced by radiation effects.