A procedure based on a finite difference method is described for calculating the temperature history of fire-exposed protected steel columns with rectangular cross section and heat generation or absorption in the insulation. Comparison with results of tests and those obtained from an analytical solution of the heat transfer equations indicates that the accuracy of the method is adequate for fire engineering purposes. The method is also suitable for the calculation of temperatures in monolithic building components such as solid concrete columns, beams, and walls. It can also be used for the calculation of temperatures of any system in which a perfect conductor or well stirred fluid is enclosed in an encasement, for example, water-filled hollow steel columns or beams, and exposed to a radiative heat source of varying temperature.