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While transmission switching is known to reduce power generation costs, the difficulty of solving even DC optimal transmission switching (DCOTS) has prevented optimal transmission switching from becoming commonplace in real-time power systems operation. In this paper, we present a k-nearest neighbors (KNN) heuristic for DCOTS which relies on the insight that, for routine operations on a fixed network, the DCOTS solutions for similar load profiles and generation cost profiles will likely turn off similar sets of lines. We take a data-driven approach and assume that we have DCOTS solutions for many historical instances, which is realistic given that the problem is solved every 5 minutes in practice. Given a new instance, we find a set of "close" instances from the past and return the best of their solutions for the new instance. We present a case study on 7 test networks ranging in size from 118 to 3,375 buses. We compare the proposed heuristic to DCOTS heuristics from the literature, commercial solver heuristics, and a simple greedy local search algorithm. In most cases, we find better quality solutions in less computational time. In addition, the computational time is within the limits imposed by real-time operations, even on larger networks. Last, we present an empirical study of our training data to understand why the heuristic works well.