[en] This paper highlights the development of a two-dimensional moving finite element transient conduction algorithm where the nodes are allowed to move in the axial direction. Typical results of the algorithm for the prediction of the rod thermal quench problem are given. The development employs a weighted residuals type method where the interpolation function is dependent on both the moving geometric position and time. Terms in the resulting equations include the unknown time rate of change of both the temperature and nodal positions. In the axial quenching of a cylindrical rod with internal heat generation, the radial positions of the nodes are frozen but the axial positions are free to move to minimize all equation residuals. Using this approach, very few nodes are required in the axial direction to reasonably follow the quenching transient. Quadrilateral ring elements (comprised of triangular ring elements) are used. The difficult external convective boundary condition used is a moving step function where the step location is determined by the quench temperature. Of special interest in the development is the use of the calculus of two-dimensional discontinuous functions in a distributional sense, system regularization, and the alteration of a stiff ordinary differential equation solver to obtain solutions