We consider theoretically the homology search between a long double-stranded DNA and a RecA-single-stranded DNA nucleofilament, emphasizing the polymeric nature of the search and the ability of double-stranded DNA to overcome the difference in pitch between itself and the nucleofilament by thermally activated stretching from the canonical B state to the metastable, stretched S state. Our analytical first-passage-time analysis agrees well with experimental data, predicts new dependencies on the intracellular fluid viscosity and ionic strength, and strongly suggests that initial homologous recognition involves a three base-pair seed.