We report the extension of measurements of the 9Be spin-lattice relaxation rate in UBe13 from 300 up to 1000 K. They reflect the fluctuating local magnetic field at the site of the 9Be nuclei. Above about 100 K, there appears a new contribution in addition to the rate observed at lower temperatures. The high temperature contribution is modeled in terms of the thermal excitation of low-lying states of the U 3+ ion along lines used by Felton et al. to explain their measurements of the specific heat. Our results indicate a splitting of 200±20 K between the ground and excited states of the system, and a lifetime of 8×10-14 s for the excited states (width =95 K).