Double-stranded DNA (dsDNA) undergoes a denaturing transition above which the strands unbind completely. At temperatures (including the physiological temperature) below the transition the base pairs tend to unbind locally, giving way to loops, i.e., locally denatured states. In the flexible-chain model, the imaginary time Schrödinger equation describes the interstrand distance distribution of dsDNA with the time variable replaced by the sequence number. We transform the equation to the Fokker-Planck equation (FPE), which provides a convenient and powerful analytical method and, via the equivalent Langevin equation, a simulation scheme. The temperature-dependent potential that emerges in the FPE manifests how the DNA conformation changes dramatically near the transition temperature. We present several simulation plots along with analytical results illustrating the order parameter (concentration of bound base pairs), base pair distance correlation function, and loop size distribution at different temperatures.