Direct numerical simulations were performed for the strongly transient and turbulent natural convection cooling of an initially isothermal quiescent liquid metal placed in a vertical cylinder in the presence of a vertical and constant magnetic field. The electrically conductive low-Prandtl number fluid is put to motion when the cylindrical wall is suddenly cooled to a uniform lower temperature. For this particular cooling process, the flow is characterized by the continuous transition among three almost discrete stages: a) development of momentum and thermal boundary layers along the vertical cold wall, b) intrusion of the cooled fluid into the main body, and c) flow and thermal stratification. The selected Rayleigh numbers in the present study are quite high such that, in the above three stages, turbulent convection is established. The numerical results show that imposing the magnetic field no observable effect is encountered at the initial stage of the vertical boundary layer development. Conduction heat transfer is favored during the intrusion stage and the cooling of the fluid is slower independently of the Rayleigh number. An interesting effect of the magnetic field is the deceleration or acceleration of the cooling process for low or high Rayleigh numbers, respectively.