The DEtection TRansformer (DETR) opened new possibilities for object detection by modeling it as a translation task: converting image features into object-level representations. Previous works typically add expensive modules to DETR to perform Multi-Object Tracking (MOT), resulting in more complicated architectures. We instead show how DETR can be turned into a MOT model by employing an instance-level contrastive loss, a revised sampling strategy and a lightweight assignment method. Our training scheme learns object appearances while preserving detection capabilities and with little overhead. Its performance surpasses the previous state-of-the-art by +2.6 mMOTA on the challenging BDD100K dataset and is comparable to existing transformer-based methods on the MOT17 dataset.