The well-known series solutions, developed in the early 19th century by Fourier (1822) in order to describe the transient process of heat conduction in a solid have since become standard tools of engineering science. Attempts have often been made to facilitate the practical use of that first mathematical theory of an irreversible process by the provision of charts and simpler approximate equations and thus avoid the cumbersome calculations involved in the series. Some of the more recent approaches to simplifying the application of Fourier’s theory are briefly reviewed. Three degrees of approximation, essentially based on the same ideas have been developed by Hausen (1942) and Elgeti (1969), by Schlunder (1972), and by the authors of this paper in 1992. Our own improved version of the approximate equations provides higher accuracy, and the additional possibility to obtain centre and surface temperatures (concentrations), not merely volumetric average values as in the earlier versions.