Thermally-induced oscillatory rarefied gas flow inside a two-dimensional rectangular cavity was investigated. The effects of the Knudsen numbers and the oscillation frequency of lid temperature on the flow parameters were analyzed. The Shakhov model equation was solved numerically based on the mesoscopic approach in the near-wall region, and the macroscopic approach was adopted in the bulk flow region to reduce the computational cost. To close the numerical iteration procedure, the velocity distribution functions, served as the pseudo boundary between macroscopic and mesoscopic methods, were reconstructed using the high-order Hermite polynomials. Numerical simulations demonstrate that the temperature profile at the central vertical of the cavity predicted by the hybrid method is in good agreement with results from the mesoscopic method, with maximum error 0.23%. Besides, the computational memory cost can be saved up to about 69.91%. The hybrid approach is able to capture the nonlinear phenomenon in the thermally-induced oscillatory rarefied gas flow under high Kn numbers, where the horizontal velocity no longer obeys the law of periodic oscillating cosine function, and the rise time of the horizontal velocity is much longer than the fall time. The thickness of the viscous penetration layer and the disturbed region increases as the Kn number increases, and decreases as the St number increases.