This research effort is related to the detailed analysis of the temporal evolution of thermal boundary layer(s) under periodic excitations. In the presence of oscillations, the nonlinear interaction leads to the formation of secondary flows, commonly known as acoustic streaming. However, the small spatial scales and the inherent unsteady nature of streaming have presented challenges for prior numerical investigations. In order to address this void in numerical framework, the development of a three-tier numerical approach is presented. As a first layer of fidelity, a laminar model is developed for fluctuations and streaming flow calculations in laminar flows subjected to traveling wave disturbances. At the next level of fidelity, two-dimensional (2D) U-RANS simulations are conducted across both laminar and turbulent flow regimes. This is geared toward extending the parameter space obtained from laminar model to turbulent flow conditions. As the third level of fidelity, temporally and spatially resolved direct numerical simulation (DNS) simulations are conducted to simulate the application relevant compressible flow environment. The exemplary findings indicate that in certain parameter space, both enhancement and reduction in heat transfer can be obtained through acoustic streaming. Moreover, the extent of heat transfer modulations is greater than alterations in wall shear, thereby surpassing Reynolds analogy.