This work investigates the potential of background-oriented schlieren tomography (3D-BOS) for the temperature field reconstruction in a non-isothermal swirling jet undergoing vortex breakdown. The evaluation includes a quantitative comparison of the mean and phase-averaged temperature field with thermocouple and fast-response resistance thermometer as well as a qualitative comparison between the temperature field and the flow field obtained from particle image velocimetry (PIV). Compared to other temperature-measuring techniques, 3D-BOS enables non-invasive capturing of the entire three-dimensional temperature field. In contrast to previous 3D-BOS applications, the present investigation makes use of the special character of the flow, which provides a global instability that leads to a rotational symmetry of the jet. Additionally, the rotational motion of the jet is used to obtain a tomographic reconstruction from a single camera. The quality of 3D-BOS results with respect to the physical setup as well as the numerical procedure is analyzed and discussed. Furthermore, a new approach for the treatment of thin occluding objects in the field of view is presented.