Before revision:  The origin of the switchingbehavior is the release of the base pairs from their confining potential as DNA denatures, which both softens the lattice and suppresses nonlinear effects and thus increases the thermal conductance .
After revision:  The origin of this rapid increase of conductance, or "switching", is the softening of the lattice and suppression of nonlinear effects as the temperature crosses the transition temperature and DNA denatures .