A temperature-dependent Schrodinger equation is proposed for the study of quantum dynamics in systems which interact with an external bath. The derivation is based on a time-dependent self consistent field (TDSCF) approximation for a system-bath wave function. As previously shown by Miller, this approximation leads to a quantum mechanical analog to the classical generalized Langevin equation. By replacing the time-evolution of the quantum mechanical bath observables with the corresponding classical trajectories, the fluctuating force and the nonlinear friction kernel in the Langevin-Schrodinger equation become temperature-dependent where the fluctuations intensity is proportional to root T. Application of the new equation to the spin-boson model shows agreement with numerically exact path integral calculations for T > 0. We relate the success of the TDSCF approximation in this case to the bath-induced noise which diminishes the importance of quantum mechanical system-bath correlations.