RICH clusters of galaxies are the largest bound masses in the Universe, but it has been difficult to determine just how massive they are(1,2). Observations of the velocities of individual galaxies, whose motions reflect the gravitational potential that they feel, have the difficulty that only the component of motion along the line of sight can be measured-the transverse component is unknown. X-ray observations seem to provide a better estimate of the mass(3-6), under the assumption that the hot X-ray-emitting gas is relaxed because of its isotropic velocity dispersion, but they have been hampered by a lack of adequate simultaneous spatial and spectral resolution. Here we present a map of the distribution of X-ray temperatures in the cluster Abell 2256, which has been thought to be nearly relaxed. Our map demonstrates that this is not the case, and implies that the assumption that the cluster is relaxed will lead to an underestimate of the true mass. As most clusters show stilt less evidence of being relaxed than A2256, their mass estimates may have larger errors.