In this work we present a new hybrid method to simulate the thermal effects of reionization in cosmological hydrodynamical simulations. The method improves upon the standard approach used in simulations of the intergalactic medium (IGM) and galaxy formation without a significant increase in the computational cost, thereby allowing for efficient exploration of the parameter space. The method uses a small set of phenomenological input parameters, and combines a seminumerical reionization model to solve for the topology of reionization with an approximate model of how reionization heats the IGM, using the massively parallel Nyx hydrodynamics code which is specifically designed to solve for the structure of diffuse IGM gas. We have produced several medium-scale, high-resolution simulations (20483, Lbox = 40 Mpc h-1) with various instantaneous and inhomogeneous ${\rm H\,{\small I}}$ reionization models that use this new methodology. We study the IGM thermal properties of these models and find that large-scale temperature fluctuations extend well beyond the end of reionization. By analysing the 1D flux power spectrum of these models, we find up to ${\sim } 50{{\rm per\cent}}$ differences in the large-scale properties (low modes, k â‰²0.01 s km-1) of the post-reionization power spectrum as a result of the thermal fluctuations. We show that these differences could allow one to distinguish between different reionization scenarios with existing Lyα forest measurements. Finally, we explore the differences in the small-scale cut-off of the power spectrum, finding that, for the same heat input, models show very good agreement provided that the reionization redshift of the instantaneous reionization model occurs at the midpoint of the inhomogeneous model.