Transient natural convective heat transfer in a paralleiogram-shaped enclosure at large Rayleigh numbers has been studied. Numerical solutions to the governing navier-Stokes equation are acquired by using a well-established finite-difference method. The possibility of utilizing this device as transient thermal diode, by means of controlling the tilt angle of the partition walls, is investigated. Comprehensive and systematic numerical results of the flow and thermal fields are presented for the tilt angle 0, 15, 30, 45 and 60 degrees ; and the Rayleigh number of $10^5,\;\;10^6$ and $10^7$. The effects of the Prandtl number and of the aspect rotio are scrutinized. Detailed time histries of the mean Nusselt number with the tilt angle is examined.