I will summarize the results of a few studies, part numerical and part analytical, that I started with J-P Eckmann and continued with K Lin and P Balint the last several years. Most of the discussion will pertain to a class of mechanical models characterized by large arrays of rotating disks and many moving particles. Energy exchange occurs at particledisk collisions. We assume the system is coupled to unequal heat reservoirs, and is in a nonequlibrium steady state. Easy-to compute algorithms for macroscopic quantities such as energy and particle density profiles are proposed, and relations between memory, finitesize effects, and geometry are discussed. We find numerically that these models, which have chaotic local dynamics, tend quickly and robustly to local thermal equilibria. To demonstrate that LTE cannot be taken for granted, I will discuss briefly a second model with “integrable” dynamics and anomolous behavior.