Knowledge about grain boundary migration is a prerequisite for understanding and ultimately modulating the properties of polycrystalline materials. Evidence from experiments and molecular dynamics (MD) simulations suggests that the formation and motion of disconnections is a mechanism for grain boundary migration. Here, grain boundary migration is modeled using a multiphase field model based on the principle of minimum dissipation potential with nonconvex boundary energy, along with a stochastic model for thermal nucleation of disconnection pairs. In this model, disconnections arise spontaneously in the presence of an elastic driving force, and that their motion mediates boundary migration. The effect is due to the fact that the formation of the disconnections pairs results in a stress concentration, causing the elastic driving force to exceed the threshold value and driving the propagation of the disconnection along the interface. The model is applied to study the propagation/annihilation of single disconnection pairs, the relaxation of a perturbed interface, and shear coupling at various temperatures. The results are consistent with the current understanding of disconnections, and capture the effect of thermal softening.