We present the first measurements of the X-ray size-temperature ( ST ) relation in intermediate redshift ( z \sim 0.30 ) galaxy clusters . We interpret the local ST relation ( z \sim 0.06 ) in terms of underlying scaling relations in the cluster dark matter properties , and then we use standard models for the redshift evolution of those dark matter properties to show that the ST relation does not evolve with redshift . We then use ROSAT HRI observations of 11 clusters to examine the intermediate redshift ST relation ; for currently favored cosmological parameters , the intermediate redshift ST relation is consistent with that of local clusters . Finally , we use the ST relation and our evolution model to measure angular diameter distances ; with these 11 distances we evaluate constraints on \Omega _ { M } and \Omega _ { \Lambda } which are consistent with those derived from studies of Type Ia supernovae . The data rule out a model with \Omega _ { M } = 1 and \Omega _ { \Lambda } = 0 with 2.5 \sigma confidence . When limited to models where \Omega _ { M } + \Omega _ { \Lambda } = 1 , these data are inconsistent with \Omega _ { M } = 1 with 3 \sigma confidence .