A methodology is presented which provides the basis for evaluating the structural response of building components, which are subjected to a complex temperature distribution, normally of the curvilinear form resulting from transient heat conduction through the thickness. An equivalent linear temperature distribution is equated by means of axial and moment equilibrium considerations. The concept is applied initially to homogeneous materials where the use of Lagrange polynomial interpolation permits explicit solutions for the equivalent thermal parameters. This formulation also leads to the optimization of sampling points for experimental measurement by the establishment of a Gauss point rule. Secondly a spreadsheet formulation is developed for the numerical solutions of more complex problems, which has utility for analysis of the response of multilayer composite constructions or scenarios where material properties are temperature dependent.