Volume diffusion (or bi-velocity) continuum model offers an alternative modification to the standard Navier-Stokes-Fourier for simulating rarefied gas flows. According to this continuum model, at higher Knudsen numbers the contribution of molecular spatial stochasticity increases. In this paper, we study a micro-cavity heat transfer problem as it provides an excellent test for new continuum flow equations. Simulations are carried out for Knudsen numbers within the slip and higher transition flow regimes where non-local-equilibrium and rarefaction effects dominate. We contrast predictions by a Navier-Stokes-Fourier model corrected by volume diffusion flux in its constitutive equations to that of the direct simulation Monte Carlo (DSMC) method and the standard Navier-Stokes-Fourier model. The results show improvement in the Navier-Stokes-Fourier prediction for the high Knudsen numbers. The new model exhibits proper Knudsen boundary layer in the temperature and velocity fields.