This work presents a simple technique for real‐time monitoring of thermal processes. Real‐time simulation‐based control of thermal processes is a big challenge because high‐fidelity numerical simulations are costly and cannot be used, in general, for real‐time decision making. Very often, processes are monitored or controlled with a few measurements at some specific points. Thus, the strategy presented here is centered on fast evaluation of the response only where it is needed. To accomplish this, classical harmonic analysis is combined with recent model reduction techniques. This leads to an advanced harmonic methodology, which solves in real time the transient heat equation at the monitored point.

In order to apply the reciprocity principle, harmonic analysis is used in the space‐frequency domain. Then, Proper Generalized Decomposition, a reduced order approach, pre‐computes a transfer function able to produce the output response for a given excitation. This transfer function is computed offline and only once. The response at the monitoring point can be recovered performing a computationally inexpensive post‐processing step. This last step can be performed online for real‐time monitoring of the thermal process. Examples show the applicability of this approach for a wide range of problems ranging from fast temperature evaluation to inverse problems.