We computationally investigate a method for spatiotemporally modulating a material's elastic properties, leveraging thermal dependence of elastic moduli, with the goal of inducing nonreciprocal propagation of acoustic waves. Acoustic wave propagation in an aluminum thin film subjected to spatiotemporal boundary heating from one side and constant cooling from the other side was simulated via the finite element method. Material property modulation patterns induced by the asymmetric boundary heating are found to be non-homogenous with depth. Despite these inhomogeneities, it will be shown that such thermoelasticity can still be used to achieve nonreciprocal acoustic wave propagation.