This paper establishes a geometric variable with which to linearize the calculation of the minimum mean time (dimensionless) necessary to reach a given mean temperature Y (dimensionless). The variable is defined by the relationship X-Gamma = [alpha(y) + alpha(z) - 2/3alpha(y)alpha(z)]. In this way the minimum mean time (minimum Fourier number) is expressed very approximately by (F) over bar (Y) = P-0 + P1XGamma. It is also determined that P-0 and P-1 are, very approximately, linear functions of the log of Y P-0 = A(0) + B-0 ln(Y), P-1 = A(1) + B(1)ln(Y). An interpolation method is further proposed for more complex geometries, built up from the "extremes" which limit or shape them. (C) 2002 Elsevier Science Ltd. All rights reserved.