The brazing stage of aluminium plate-fin heat exchangers is a high temperature industrial process in a vacuum furnace. To prevent mechanically dangerous thermal gradients into the load during the heating, a regulation system calculates the heating setpoint of each radiant panel of the furnace by exploiting the measurements of dozens of thermocouples on the surface of the load. Unfortunately, a thermocouple breakdown may mislead the regulation system. A possible solution to this recurring metrological problem lies in the use of virtual sensors, that is mathematical models which mimic measurements of real sensors and can therefore substitute defective thermocouples. This study concerns the identification of ARX autoregressive parametric models to get such virtual sensors. To find the best ARX models for each thermocouple, the approach is to find the best inputs and orders. First, the influential physical quantities are selected, particularly among radiant panel heating powers. Next, the selected heating powers are merged into a single average-input with weighting coefficients chosen by particle swarm optimization. Finally, the ARX model orders are determined. The last two steps are carried out simultaneously by minimizing a criterion based on the Akaike Information Criterion, in order to balance accuracy and parsimony of the models. In this paper, ARX models are identified on numerical data from the detailed model of a typical load, and then on real data from the brazing process of this load. With numerical data, ARX models are very accurate (fit between model and measurement over 99%). With real data, ARX models remain accurate (fit over 95%). These models are parsimonious: their parameter number is less than 20.