This paper presents a statistical mechanical analysis of strand separation in a topologically constrained (i.e., superhelical) DNA homopolymer. Our calculations show that positive superhelicity can efficiently stabilize the B-form DNA duplex at temperatures substantially above the transition temperature [Formula Presented] for denaturation of the linear molecule. Moderate superhelix densities (σ<0.08) suffice to keep a DNA molecule virtually entirely in the B-form conformation at temperatures where, if it were relaxed, it would be substantially denatured. This behavior persists up to a predicted critical temperature [Formula Presented]>[Formula Presented]. When T>[Formula Presented] the molecule remains entirely denatured regardless of the amount of superhelicity imposed. The value of [Formula Presented] is shown to depend on the torsional stiffness C associated with interstrand twisting of the unpaired strands within denatured regions. Thus, experiments that measure [Formula Presented] would provide another method to evaluate C.