Although effective cooling of micro-electro-mechanical systems (MEMS) with oscillatory components is essential for reliable device operation, the role of oscillation on heat transfer remains poorly understood. In this work, heat and mass transfer of the oscillatory gas flow inside a square cavity is computationally studied by solving the Boltzmann model equation, i.e. the Shakhov model. The oscillation frequency of the lid and rarefaction and nonlinearity of the flow field are systematically investigated. Our results show that, when the oscillation frequency of the lid increases, the usual cold-to-hot heat transfer pattern for highly rarefied flow changes to hot-to-cold, which contradicts the well-known anti-Fourier (i.e. cold-to-hot) heat transfer in a non-oscillatory lid-driven cavity. In addition, the thermal convection will be dramatically enhanced by lid oscillation, which may play a dominant role in the heat transfer. Meanwhile, the average Nusselt number varies non-monotonically with the oscillation frequency, with the maximum occurring at the anti-resonance frequency. Finally, the average Nusselt number on the lid at various oscillation frequencies is found to reduce when the gas becomes more rarefied. These findings may be useful for the thermal design of MEMS. (C) 2018 The Authors. Published by Elsevier Ltd.