When a solid is exposed to a hot gas or liquid, the resistance to heat transfer in the fluid is usually significant, and the surface temperature changes with time. In this work, an attempt has been made to formulate a simple-to-use method for one-dimensional heat flow with variable surface temperatures in slabs and spheres as a function of the Fourier number and the Biot number in order to arrive at the temperature distribution in the solid and the average solid temperature changes with time. The average absolute deviation between the reported data and the proposed correlations are found to be 1.8%. (C) 2010 Elsevier Ltd. All rights reserved.