Over the past years, tracking in the visible domain has seen rapid growth by exploiting Deep Neural Network (DNN) based methods, whereas, tracking in the Thermal Infrared (TIR) domain has seen a small interest. In this comparative study, we address tracking in a TIR maritime context for surveillance applications. Towards this end, we first compare the performances of traditional Single Object Trackers (SOTs) and recent DNN-based SOTs on a TIR maritime data set. Following this, we examine the sequences of the TIR data set causing difficulties for trackers and identify problematic attributes. Firstly, We use a group constituted of recent state-of-the-art DNN-based trackers and another group constituted of traditional trackers not employing DNN-based methods, and measure performance using the following metrics: Intersection over Union (IoU), center error, success rate, and robustness. Furthermore, we rank the trackers by taking into account their scores on IoU and robustness. The presented study shows that recent trackers exploiting DNNs methods for tracking perform on average better: over 24% on IoU and over 14% on robustness than their counterparts not utilizing DNN in their tracking process. Moreover, despite the provided improvement by using DNN-based trackers, a failure case analysis shows that clutter, occlusion handling, low-resolution and scale change of the target, are visual attributes that still remain challenging, requiring further improvement.