A numerical study of wave propagation through gases with non-uniform temperature distributions is presented. The concept of using regions of hot gas inside an ambient environment has potential in aeroacoustic applications, such as jet screech mitigation. The main objective of this study is to determine the impact of temperature gradients on high-intensity, initially sinusoidal pressure waves. Particular emphasis is paid to wave reflection, transmission, and any influence a high temperature region may have on nonlinear behavior. Ultimately, the performance of thermal barriers in attenuating nonlinear waves is evaluated. This analysis considers the one-dimensional compressible unsteady Euler's equations with an ideal gas state equation. The shape and extent of the high temperature zone is varied to study the effect of this region on wave propagation. Wave reflection and transmission is studied for a range of wave and thermal field parameters. Results for non-linear pressure waves are compared to linear acoustic waves.