Transient temperature solutions in plates are derived for heating conditions varying as time. to an integer power at a surface. The powers include 0, 1, 2 and 3; the last of which is useful for cubic splines. Boundary conditions of the first, second and third kinds are treated at both surfaces with the non-homogeneity at x = 0. As the power increases by one, all additional quasi-steady summation term appears in the analytical solution. Algebraic forms for these summations are derived in a systematic way. Extensive tables are given along with all example. (c) 2007 Elsevier Ltd. All rights reserved.