  We present a Bayesian inference analysis of the Markevitch (1998) and Allen &
Fabian (1998) cooling flow corrected X-ray cluster temperature catalogs that
constrains the slope and the evolution of the empirical X-ray cluster
luminosity-temperature (L-T) relation. We find that for the luminosity range
10^44.5 erg s^-1 < L_bol < 10^46.5 erg s^-1 and the redshift range z < 0.5,
L_bol is proportional to T^2.80(+0.15/-0.15)(1+z)^(0.91-1.12q_0)(+0.54/-1.22).
We also determine the L-T relation that one should use when fitting the Press-
Schechter mass function to X-ray cluster luminosity catalogs such as the
Einstein Medium Sensitivity Survey (EMSS) and the Southern Serendipitous High-
Redshift Archival ROSAT Catalog (Southern SHARC), for which cooling flow
corrected luminosities are not determined and a universal X-ray cluster
temperature of T = 6 keV is assumed. In this case, L_bol is proportional to
T^2.65(+0.23/-0.20)(1+z)^(0.42-1.26q_0)(+0.75/-0.83) for the same luminosity
and redshift ranges.
