A general framework is developed for the simulation of nonisothermal statistical-mechanical ensembles. This framework is intended to synthesize the formulation of advanced Monte Carlo simulation methods such as multihistogram reweighting, replica-exchange methods, and expanded ensemble techniques so that they can be applied to different nonisothermal ensembles. Using Lennard-Jones systems as test cases, novel implementations of these methods are demonstrated with different ensembles including the microcanonical, isobaric-isoenthalpic, and isobaric-semigrand ensembles. In particular, it is shown that the use of multiensemble methods allows the efficient simulation of microcanonical density of states, entropies, vapor-liquid and solid-liquid equilibrium for pure component systems, and fluid-phase coexistence for binary mixtures. In these applications, comparisons are also presented that highlight the advantages of the proposed multiensemble implementations over alternative methods used before. (C) 2005 American Institute of Physics.