This paper describes the unsteady convective flow of a supercritical fluid in Rayleigh-Benard configuration using direct numerical simulation. Two- dimensional earlier studies reported fast temperature equilibrium due to the piston effect and the development of a convective instability when the local Rayleigh number exceeds a critical value. In the present work, a high order 3D finite volume method has been developed and optimized, the code has been thoroughly validated, and to our knowledge, we show for the first time a three- dimensional convective instability in a supercritical fluid. Inspecting the time-evolution of temperature field patterns, we show the time-transition to convection-dominated flow causing the collapse of the boundary thermal layers, we exhibit corner effects and the three-dimensional behavior of the flow, and we show the heating intensity effects on the temperature field structure.