We investigate the predicted present-day temperature profiles of the hot , X-ray emitting gas in galaxy clusters for two cosmological models - a current best-guess \Lambda CDM model and standard cold dark matter ( SCDM ) . Our numerically-simulated “ catalogs ” of clusters are derived from high-resolution ( 15 h ^ { -1 } kpc ) simulations which make use of a sophisticated , Eulerian-based , Adaptive Mesh-Refinement ( AMR ) code that faithfully captures the shocks which are essential for correctly modelling cluster temperatures . We show that the temperature structure on Mpc-scales is highly complex and non-isothermal . However , the temperature profiles of the simulated \Lambda CDM and SCDM clusters are remarkably similar and drop-off as T \propto ( 1 + r / a _ { x } ) ^ { - \delta } where a _ { x } \sim r _ { vir } / 1.5 and \delta \sim 1.6 . This decrease is in good agreement with the observational results of Markevitch et al . ( 1998 ) but diverges , primarily in the innermost regions , from their fit which assumes a polytropic equation of state . Our result is also in good agreement with a recent sample of clusters observed by Beppo SAX though there is some indication of missing physics at small radii ( r < 0.2 r _ { vir } ) . We discuss the interpretation of our results and make predictions for new x-ray observations that will extend to larger radii than previously possible . Finally , we show that , for r > 0.2 r _ { vir } , our universal temperature profile is consistent with our most recent simulations which include both radiative cooling and supernovae feedback .