A numerical study is made of transient natural convective cool-down process of air under gravity and magnetizing force in a closed cylindrical cavity. An inhomogeneous magnetic field calculated by Biot-Savart's law exerts a magnetizing force on material of high magnetic susceptibility, like a oxygen gas(paramagnetic) in a temperature gradient field. Cooling is accomplished by abruptly lowering the sidewall temperature under strong magnetic field. Computation results without gravity reveal that transient characteristics of stream functions and isotherms change by varying the radius and axial position of a coil. When magnetizing force is parallel to gravity, the maximum of stream function is increased and cooling time is decreased. When magnetizing force is opposed to gravity, as magnetizing force is increased, the maximum of stream function is decreased and cooling time is increased in gravity is dominant, whereas the maximum of stream function is increased and cooling time is decreased in magnetizing force is dominant. The analysis of transient characteristics of cool-down process suggests that magnetizing force can enhance or suppress thermal convection and heat transfer.