Thermal Bridges on Building Rooftops (TBBR) is a multi-channel remote sensing dataset. It was recorded during six separate UAV fly-overs of the city center of Karlsruhe, Germany, and comprises a total of 926 high-resolution images with 6927 manually-provided thermal bridge annotations. Each image provides five channels: three color, one thermographic, and one computationally derived height map channel. The data is pre-split into training and test data subsets suitable for object detection and instance segmentation tasks. All data is organized and structured to comply with FAIR principles, i.e. being findable, accessible, interoperable, and reusable. It is publicly available and can be downloaded from the Zenodo data repository. This work provides a comprehensive data descriptor for the TBBR dataset to facilitate broad community uptake.