We describe a technique for the rapid and reliable prediction of outputs of interest, of elliptic partial differential equations with affine parameter dependence. To achieve efficiency, the reduced-basis method is used; reliability is obtained by the development of relevant a posteriori error estimators. We apply this method to the problem of designing a thermal fin, to effectively remove heat from a surface. A number of design parameters=inputs are considered. Each possible configuration, corresponding to different choices of the design parameters, needs to be evaluated by solving the heat conduction equation and calculating certain outputs of interest like the average temperature on the fin base.