We report the application of a new Monte Carlo method, Smoothed Particle Inference (SPI, described in a pair of companion papers), towards analysis and interpretation of X-ray observations of clusters of galaxies with the XMM-Newton satellite. Our sample consists of publicly available, well-exposed observations of clusters at redshifts z > 0.069, totaling 101 objects. We determine the luminosity and temperature structure of the X-ray emitting gas, with the goal to quantify the scatter and the evolution of the L_X - T relation, as well as to investigate the dependence on cluster substructure with redshift. We confirm that L_X \propto T^3 and we find a weak redshift dependence (\propto (1+z)^(\beta_LT), \beta_LT=0.50 +- 0.34), in contrast to some Chandra results. The level of dynamical activity is established using the "power ratios" method, and we find signs of evolution in the P_3/P_0 power ratio. A new method, the "temperature two-point correlation function," is proposed. This method is used to determine the "power spectrum" of temperature fluctuations in the X-ray emitting gas as a function of spatial scale. We show how this method can be fruitfully used to identify cooling core clusters as well as those with disturbed structures, presumably due to on-going or recent merger activity. Show Partial Abstract