This paper presents a multi-stage optimal power flow (OPF) approach for efficient management of contingencies, in which dynamic thermal models of overhead lines and power transformers are used to evaluate maximum lead time (MLT) available to network operators to resolve violated post-contingency constraints. At the first stage, optimal settings of volt-var controls, such as transformers with on-load tap changers and shunt capacitors, are selected, taking into account voltage-dependent load models. The second stage provides optimal generation re-dispatch, including fast-start generators. At the final third stage, optimal load shedding is implemented to clear all remaining constraint violations. The OPF problem is solved by a hybrid metaheuristics method and illustrated on a modified IEEE 14-bus network. Obtained results demonstrate that presented method can help network operators to efficiently resolve all violated constraints within the available MLT.