Uranus’ thermospheric temperature has been observed to decrease with time since 1990. The effect of this steady cooling on its exospheric density distribution and escape is yet to be determined. Characterizing Uranus’ exospheric behavior is essential towards planning future Ice Giant missions. At present, there is little understanding of Uranus’ exospheric dynamics and its evolution with seasons as no studies have been conducted after the initial Voyager 2’s visit to the Ice Giant in 1986. The Voyager 2 data did reveal substantial gas densities of 108 cm-3 at radial distances of ~2 Uranus radii. It also detected energetic H atoms at temperatures of 23,000 K at distances of 8 Uranus radii. The evolution of this H population with time is not known. A substantial series of observations of Uranus in the ultraviolet exist with the Hubble Space Telescope covering a period of ~22 years. These include both images with the Advanced Camera for Surveys (ACS) and spectra with the Space Telescope Imaging Spectrograph (STIS). We have analyzed these HST images of Uranus to isolate the solar Lyman alpha photons resonantly scattered by Uranus’ exospheric H atoms. We will present the time evolution of the observed Lyman-alpha intensity at Uranus and discuss the correlation of exospheric H density distribution with Uranus’ thermospheric cooling.