We present a theoretical model for long-range triplet excitation energy transfer in DNA sequences of alternating adenine-thymine steps. It consists of thermally induced hops through thymine bases. Intrastrand hops between thymines separated by an AT step are preferred to interstrand hops between thymines in consecutive steps. Our multi-step mechanism is consistent with recent results (L. Antusch, N. Gass and H.-A. Wagenknecht, Angew. Chem., Int. Ed., 2017, 56, 1385-1389) describing a shallow dependence of triplet sensitized DNA damage relative to the distance between the sensitizer and the reacting thymine-thymine pair.