In this study, the nonequilibrium effects at the stagnation wall in one-dimensional unsteady microflow responding to the external sinusoidal oscillation are investigated. The fluctuating behavior of the rarefied medium is simulated by employing the unsteady DSMC method under various conditions with different acoustic Reynolds and Knudsen numbers. As a result, it is found that the nonequilibrium effect exists at the stagnation wall, especially when the gas density number is small. Due to such a nonequilibrium effect found in a fluctuating medium, the Knudsen number representing system size becomes a more important system parameter than the acoustic Reynolds number even for the constant excitation frequency. Also, the validity of the well-known Maxwell-Smoluchowski relation and its higher-order modifications are tested by comparing the heat fluxes from these relations with the direct DSMC result.