ASCA data are used to obtain two-dimensional gas temperature maps of the hot non-cooling flow clusters A2256 , A2319 , A2163 and A665 . In all four clusters , the temperature decreases significantly at off-center distances of \sim 1 h ^ { -1 } Mpc ( H _ { 0 } \equiv 100 h km s ^ { -1 } Mpc ^ { -1 } ) . Central regions of the two nearer clusters A2256 and A2319 are resolved by ASCA and appear largely isothermal except for the cooler spots coincident with the subunits in their X-ray surface brightness . Although the existence of this substructure may suggest ongoing merger activity , no asymmetric features in the temperature distribution resembling those in the hydrodynamic merger simulations ( e.g. , Schindler & Müller 1993 ) are apparent . In the outer parts of the clusters , the temperature declines symmetrically with radius . In A2256 and A2319 , it follows a polytropic slope with \gamma \simeq 1.3 - 1.5 . This is somewhat steeper than the simulations predict for a flat CDM universe and is closer to the open universe predictions ( Evrard et al . 1996 ) . The temperature drop is more prominent in the outer regions of A2163 and A665 and appears even steeper than adiabatic ( although not inconsistent with it ) . If the gas in the outskirts of these two clusters is indeed as cool as we measure , the cluster atmospheres should be convectively unstable and transient . Also , such a steep temperature profile could not possibly emerge if the gas was heated only via the release of its own gravitational energy during infall . This may indicate the presence of an additional heat source in the inner cluster , such as merger shocks transferring energy from the dark matter to the gas . The results suggest that A2256 and A2319 are pre-merger systems and A2163 and A665 are ongoing or post-mergers .