Modern approaches dedicated to controlling the operation of gas foil bearings require advanced measurement techniques to comprehensively investigate the bearings’ thermal and thermomechanical properties. Their successful long-term maintenance with constant operational characteristics may be feasible only when the allowed thermal and mechanical regimes are rigorously kept. Hence, an adequate acquisition of experimental readings for the critical physical quantities should be conducted to track the actual condition of the bearing. The above-stated demand has motivated the authors of this present work to perform the thermomechanical characterization of the prototype installation of a gas foil bearing, applying a specialized sensing foil. This so-called top foil is a component of the structural part of the bearing’s supporting layer and composed of a superalloy, Inconel 625. The strain and temperature distributions were identified based on the readings from the strain gauges and integrated thermocouples mounted on the top foil. The measurements’ results were obtained for the experiments that represent the arbitrarily selected operational conditions of the tested bearing. Specifically, the considered measurement scenario relates to the operation at a nominal rotational speed, i.e., during the stable process, as well as to the run-up and run-out stages. The main objectives of the work are: (a) experimental proof for the described functionalities of the designed and manufactured specialized sensing foil that allow for the application of a novel approach to the bearing’s characterization, and (b) qualitative investigation of the relation between the mechanical and thermal properties of the tested bearing, using the measurements conducted with the newly proposed technical solution.