************************************************************************* 52177 We are proposing to complete our program to measure the X-ray temperatures (Tx) of X-ray luminous, distant (z>0.5) clusters of galaxies. The final cluster in our sample, MS1137+66 (z=0.78), is just as luminous but optically much poorer than the other 3 clusters. The distant clusters observed thus far in our sample are hotter than standard structure formation models predict. Cluster temperatures at high redshift constrain predictions of Lx-Tx evolution. Because MS1137+66 is chosen from a well-defined X-ray selected sample, its Tx also constrains the z=0.8 cluster temperature function. It is bright and compact enough for 1-CCD SIS observations; the temperature break is redshifted to ~3-5 keV. HST WFPC2 and ROSAT HRI images are scheduled for MS1137+66. *************************************************************************