A new transfinite element methodology for nonlinear transient thermal analysis is described. The proposed methodology is a hybrid approach that combines the major advantages of finite-element techniques, classical Bubnov-Galerkin schemes, and transform methods. Fundamental concepts of the methodology, including recent developments for application to nonlinear thermal problems, are described in technical detail. The applicability of the hybrid transfinite element approach to nonlinear transient thermal problems is quite novel. Comparative results of several test problems validate the basic capabilities of the proposed formulations. The hybrid transfinite element approach proposed here provides a computational methodology for nonlinear transient thermal analysis and has the potential for further extension.