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A local Maxwellian thermostat for the multiparticle collision dynamics algorithm is proposed. The algorithm is based on a scaling of the relative velocities of the fluid particles within a collision cell. The scaling factor is determined from the distribution of the kinetic energy within such a cell. Thereby the algorithm ensures that the distribution of the relative velocities is given by the Maxwell-Boltzmann distribution. The algorithm is particularly useful for non-equilibrium systems, where temperature has to be controlled locally. We perform various non-equilibrium simulations for fluids in shear and pressure-driven flow, which confirm the validity of the proposed simulation scheme. In addition, we determine the dynamic structure factors for fluids with and without thermostat, which exhibit significant differences due to suppression of the diffusive part of the energy transport of the isothermal system.