We present an analysis of a 72 ks Chandra observation of the double cluster Abell 1644 (z=0.047). The X-ray temperatures indicate the masses are M500=2.6+/-0.4 x10^{14} h^{-1} M_sun for the northern subcluster and M500=3.1+/-0.4 x10^{14} h^{-1} M_sun for the southern, main cluster. We identify a sharp edge in the radial X-ray surface brightness of the main cluster, which we find to be a cold front, with a jump in temperature of a factor of ~3. This edge possesses a spiral morphology characteristic of core gas sloshing around the cluster potential minimum. We present observational evidence, supported by hydrodynamic simulations, that the northern subcluster is the object which initiated the core gas sloshing in the main cluster at least 700 Myr ago. We discuss reheating of the main clusters core gas via two mechanisms brought about by the sloshing gas: first, the release of gravitational potential energy gained by the cores displacement from the potential minimum, and second, a dredging inwards of the outer, higher entropy cluster gas along finger-shaped streams. We find the available gravitational potential energy is small compared to the energy released by the cooling gas in the core.
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