Undersea gliders are autonomous undersea vehicles (AUVs) that travel the world's oceans in a sawtooth climb-dive pattern. These gliders are driven by buoyancy engines that typically use electrically powered pumps to displace water with an oil bladder and thus enable a buoyancy change. Battery capacity limits the endurance of these types of engines and vehicles. The Argo project uses similar electrical buoyancy engines to help monitor climate change . Increasing the endurance of buoyancy engines could have an impact on sensors deployed in the world's oceans by decreasing the maintenance cost of sensing missions and allowing for studies to be conducted over a longer period of time. Buoyancy heat engines driven by the naturally occurring thermocline that exists over a large expanse of the world's oceans can drastically improve endurance. These engines harness environmental energy as opposed to consuming electrical energy to change vehicle buoyancy. Buoyancy engines have been developed that employ the volume change produced during the phase change of wax , but it may also be possible to use the oceanic thermocline to drive a buoyancy heat engine based on shape memory alloys (SMA's) (Fig. 1). Shape memory alloys can recover a large amount of applied strain, up to approximately 10% , when heated due to a solid state phase transformation in the alloy. The high strain energy of shape memory alloys can be leveraged to create a lighter and more efficient buoyancy heat engine, but the performance and capability of a solid state SMA based engine is unknown. Previous work has discussed the analysis, design, and testing of such an engine, called the shape memory alloy buoyancy heat engine (SMA-BHE) . This paper will examine the dynamics of the SMABHE by coupling a lumped system heat transfer model and the Brinson model for one-dimensional SMA constitutive behavior to the kinematics of a notional undersea glider in an ocean environment. Including the Brinson model and other known SMA relations in the kinematic simulation of a notional glider led to a model that predicted successful AUV operation with a SMA-BHE at depths past 700 m.