Green’s function technique (GFT) is largely used for on-line calculation of thermal stresses in machines and plants; it allows directly turning parameters such as fluid temperatures, pressures and flow rates in thermal stresses. Recently the use of the GFT is extended by the authors to cases having variable convective coefficients. The novel methodology is made of two steps: first of all boundary temperatures are evaluated by time integration of a reduced thermal model and then thermal stresses are calculated by means of the GFT using as inputs the boundary temperatures previously evaluated. The new approach implies a large number of convolution integrals for thermal stress calculation. In order to reduce computation time it is proposed to convert the convolution integrals which characterize the GFT into time integration of an equivalent system of uncoupled first order differential equations, whose coefficients are estimated fitting Green’s functions with a sum of exponential terms.