[en] The use of high temperature superconductors (HTS) in magnets operating at high temperatures, such as 20 K or 77 K, has not yet occurred because of the low critical currents. Projections of characteristics and performance of high temperature superconductors have been made to indicate potential and point out specific research areas. Initial estimates have identified the small thermal conductivity of HTS as one of the important physical parameters determining stability limitations. In this paper, the impact of HTS small thermal conductivity upon recovery currents is discussed. A simple model equating heat production in high temperature superconductors during current sharing to heat transport or cooling of the superconductor predicts recovery currents. In some cases the small superconductor thermal conductivity, and not the surface cooling, limits the heat transport out of the superconductor. The presence of a stabilizer decreases heat generation in the superconductor during current sharing, thus increasing the recovery currents compared to bare superconductors