State-of-the-art thermal infrared cameras produce high quality images with a bit depth of up to 16 bits per pixel (bpp). In practice, the data often reach a bit depth of 14 bpp, which cannot be displayed naively to a standard monitor that is limited to 8 bpp. Therefore, the dynamic range of these images has to be compressed. This can be done with an operator called tone mapping. There are many methods available for tone mapping, but the quality of the results can be extremely different. In this paper, we discuss and evaluate image quality assessment measures for tone mapping taken from the literature using thermal infrared videos. The usefulness of the measures is analyzed and effectively demonstrated by utilizing various reference Tone Mapping Operators (TMOs) based on traditional algorithm engineering on the one hand and deep learning on the other hand. We conclude that the chosen measures can objectively assess the quality of TMOs in thermal infrared videos.