Have you guys that responded spent much time in tropical waters? While snorkeling or diving, you can cruise through temperature variations as much as 10 degrees in a few feet. There are some spots that we do both in Hawaii that have haloclines and thermoclines that are swirled through a bay. While following a fish, they generally cruise along in a straight line through multiple temperature and salinity variations and it has no effect on them. They don't bob and weave, looking to stay in one temperature or salinity zone. How do I know where there is a salinity variation? You can see it in the water. The upper water will be colder and blurry, go down 2-3 feet and its clear and much warmer. The bigger issue in the aquarium is that these variations are another stress factor that can contribute to disease so we try to minimize variations in order to maintain the most consistent environment we can, keeping the immune systems of the fish as strong as possible by decreasing their needs to compensate for variations. In the natural environment, the fish have less stress factors and can shake these fluctuations off much easier than in our aquariums.
Regarding the fish staying above the thermocline for more oxygen, warmer water holds less oxygen, so your comment doesn't really work. If oxygen was the concern for the fish, they would stay below the thermocline, where the cooler water would hold more oxygen and where their metabolism would be lower, using less oxygen.
not trying to come off as a know it all here, just trying to give the OP the best answer possible.