This thesis addresses the problem of tracking a thermocline---a layer of water showing an intense vertical temperature gradient---with an Autonomous Underwater Vehicle (AUV). One of Florida Atlantic University's Ocean Explorer (OEX) AUV has been upgraded, as part of the work described here, by integration of a standard and convenient software interface, and used in several thermocline survey experiments aimed at gathering oceanographic data relevant to thermoclines. A tool that simulates the longitudinal motion of the OEX through a water slice, whose temperature map is read using a simulated temperature and depth sensor, has been developed. Using this tool and information from at-sea experiments, several control methods for the OEX to track a thermocline were analyzed. In particular, two different algorithms were implemented and tested by simulation. Overall, two control algorithms have been validated, and it will soon be possible to provide the AUV with a thermocline tracking capability.