Recent investigations have shown that the temperature variation caused by sinusoidal loading of a solid consists of two harmonic components. In this paper it is shown that by using an appropriate Airy stress function the separated stress components can be obtained, almost always, with knowledge of these two components. Since the second harmonic response is small compared to the noise level, the question of experimental design is examined. The problem of uniqueness is also studied. The close similarity between the second harmonic response and various energy parameters is also investigated and its role in structural optimization is discussed. The method is demonstrated on a particular example using simulated noisy data.