The dynamo model of solar magnetic field generation assumes that magnetic flux is retained at the dynamo site for times of the order of the solar-cycle period. However, flux tubes in the solar convection zone are expected to be buoyant, rising to the surface on timescales much shorter than the solar cycle. Since the initial 1955 paper by Parker on this puzzle, there have been numerous investigations into the detailed physics of buoyant flux tubes, but no definitive conclusions have yet been reached. We investigate the role of thermal conduction in flux tube dynamics using MHD simulations. We expect that the thermal conductivity can vary with conditions inside the tube relative to those in the ambient fluid and that such variation in turn affects the tube's energetics and evolution. Preliminary results suggest that suppressed thermal conductivity inside the tube can significantly affect tube morphology and evolution, depending on the characteristics of the tube and its surroundings. We discuss possible implications of our results for solar surface magnetic fields. D.D.L. acknowledges support from an NSF-NATO Postdoctoral Fellowship in Science and Engineering. We thank Thierry Emonet for helpful discussions. We are grateful to Mark Rast for the use of his MHD code. The numerical simulations were performed on the Cray T3E at CIEMAT in Madrid, Spain.