The problem of transient conduction in an unclad fuel plate with negligible surface resistance was solved analytically for the case wherein simultaneous step changes are made in the volume distributed heat generation rate and the surface temperatures. The solutions for the central (maximum) fuel temperature and the space-mean temperature are presented in graphs. A solution for the case of an arbitrary number of successive step changes was obtained by superposition (example), and an approximate solution for the case of arbitrarily and continuously varying heat release rate and surface temperatures coupled to the reactivity was discussed.