This paper addresses the problem of controlling the temperature of an air heating fan with an unknown flow input rate. This time-varying uncertainty in the dynamics of the plant significantly reduces the performance of the closed-loop system, if a single (fixed) non-adaptive controller is used. Moreover, the average temperature of the air flowing through the system, that can be seen as an offset on the corresponding dynamics, is also (slowly) time-varying and highly dependent on the ambient temperature. Therefore, an alternative approach to this problem is proposed, by resorting to a novel multiple-model adaptive control methodology that relies on set-valued observers to identify the operating region of the plant. The suggested method is evaluated experimentally, demonstrating a loss of performance of about 2% when compared to the (unrealizable) perfect model identification scenario. As a shortcoming, the computational requirements due to the use of SVOs are considerably larger than the ones needed for an LTI non-adaptive controller.