Cameras digitize real-world scenes as pixel intensity values with a limited value range given by the available bits per pixel (bpp). High Dynamic Range (HDR) cameras capture those luminance values in higher resolution through an increase in the number of bpp. Most displays, however, are limited to 8 bpp. Naïve HDR compression methods lead to a loss of the rich information contained in those HDR images. In this paper, tone mapping algorithms for thermal infrared images with 16 bpp are investigated that can preserve this information. An optimized multi-scale Retinex algorithm sets the baseline. This algorithm is then approximated with a deep learning approach based on the popular U-Net architecture. The remaining noise in the images after tone mapping is reduced implicitly by utilizing a self-supervised deep learning approach that can be jointly trained with the tone mapping approach in a multi-task learning scheme. Further discussions are provided on denoising and deflickering for thermal infrared video enhancement in the context of tone mapping. Extensive experiments on the public FLIR ADAS Dataset prove the effectiveness of our proposed method in comparison with the state-of-the-art.