Entropy-driven demixing transitions play an important role in a variety of phenomena in solution chemistry, in mixtures of ionic liquids, in polymers, and in biosystems. A simple coarse-grained model of a binary (A and B) fluid mixture of Lennard-Jones particles carrying classical harmonic oscillators whose frequency decreases with increasing homo-coordination separates into two nearly pure phases with increasing T, as the entropy gain in lowering the oscillators' frequency overcomes the potential energy and ideal entropy advantage of the homogeneous phase. We characterize features of the demixing transition and outline physical questions that can be addressed by this simple and inexpensive model. Besides and beyond these conceptual points, we provide examples of how the model could be adapted to real systems, aiming at their quantitative description by a coarse-grained model made of particles carrying momentum, energy, and entropy.