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We derive a Markov chain Monte Carlo algorithm for data detection in multi-antenna systems. The proposed algorithm is based on the Rao-Blackwellization principle, and is parameterized by a value eta that can be interpreted as a system temperature. We demonstrate by simulations that systems with increased temperature (η>;1) significantly outperform the straightforward choice of η=1. Due to its log-domain formulation, our algorithm combines near-optimal performance with low implementation complexity.