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This paper proposes a kernel for the distributed simulation of real-time systems modelled by Merlin and Farber's time Petri nets (TPN). The realization depends on temporal uncertainty time warp (TUTW), a novel time warp algorithm capable of exploiting temporal uncertainty in general optimistic simulations. A key feature of the application rests on the fact that TPN models naturally exhibit a certain degree of temporal uncertainty which the TUTW control engine can exploit to achieve good speedup without impairing accuracy of the simulation output. Usefulness of the achieved TUTW/TPN kernel is demonstrated by simulation experiments on a real-time system example.