Kinetic theory provides a rigorous foundation to explore the unsteady (oscillatory) flow of a dilute gas, which is often generated by nanomechanical devices. Recently, formal asymptotic analyses of unsteady (oscillatory) flows at small Knudsen numbers have been derived from the linearised Boltzmann–Bhatnagar–Gross–Krook (Boltzmann–BGK) equation, in both the low- and high-frequency limits (Nassios & Sader, J. Fluid Mech., vol. 708, 2012, pp. 197–249 and vol. 729, 2013, pp. 1–46; Takata & Hattori, J. Stat. Phys., vol. 147, 2012, pp. 1182–1215). These asymptotic theories predict that unsteadiness can couple strongly with heat transport to dramatically modify the overall gas flow. Here, we study the gas flow generated between two parallel plane walls whose temperatures vary sinusoidally in time. Predictions of the asymptotic theories are compared to direct numerical solutions, which are valid for all Knudsen numbers and normalised frequencies. Excellent agreement is observed, providing the first numerical validation of the asymptotic theories. The asymptotic analyses also provide critical insight into the physical mechanisms underlying these flow phenomena, establishing that mass conservation (not momentum or energy) drives the flows – this explains the identical results obtained using different previous theoretical treatments of these linear thermal flows. This study highlights the unique gas flows that can be generated under oscillatory non-isothermal conditions and the importance of both numerical and asymptotic analyses in explaining the underlying mechanisms.