These fish are not able to pump water through their gills if they are not swimming. Therefore, they do not stop moving even for a moment during their entire lives. They even swim while sleeping, although they do it much more slowly, moving slowly enough to make water pass through their gills.
Tuna, like mammals and birds, are homeothermic (warm-blooded) animals. This means that they are able to maintain their body temperature a few degrees above or below the environment temperature.