Simple equations were developed to predict the values of some characteristic transcendental and Bessel functions, and hence the temperature history in regular solid foods of finite and infinite dimensions under unsteady state conduction with convective heat transfer at the surface. For various combinations of Biot (0.02- 200) and Fourier (>0.2) numbers, the mean error involved in predicting the unsteady temperature ratio using the developed equations was less than 0.1% as compared to the original models. Equations were presented for temperature at any location as well as the mass average temperature. The characteristic functions were related to the f and j parameters from heating and cooling curves.