The Planck system of units has been recognized as the most fundamental such system in physics ever since Dr. Max Planck first derived it in 1899. The Planck system of units in general, and especially the Planck power in particular, suggest a simple and interesting cosmological model. Perhaps this model may at least to some degree represent the real Universe; even if it does not, it seems interesting conceptually. The Planck power equals the Planck energy divided by the Planck time, or equivalently the Planck mass times c 2 divided by the Planck time. We show that the nongravitational mass-energy of our local region (L-region) of the Universe is, at least approximately, to within a numerical factor on the order of 2, equal to the Planck power times the elapsed cosmic time since the Big Bang. This result is shown to be consistent, to within a numerical factor on the order of 2, with results obtained via alternative derivations. We justify employing primarily L-regions within an observer's cosmological event horizon, rather than O-regions (observable regions) within an observer's cosmological particle horizon. Perhaps this might imply that as nongravitational mass-energy leaves the cosmological event horizon of our L-region via the Hubble flow, it is replaced at the rate of the Planck power and at the expense of negative gravitational energy. Thus the total mass-energy of our L-region, and likewise of all L-regions, is conserved at the value zero. Some questions concerning the Second Law of Thermodynamics and possible thwarting of the heat death of the Universe predicted thereby, whether via Planck-power input or via some other agency, are discussed.