We examined, by three-dimensional numerical computations, the magnetothermal convection of air (a paramagnetic substance) enclosed in a cylindrical vessel with a Rayleigh-Benard model under the application of an axisymmetric magnetic force at the center of a solenoidal superconducting magnet. Axisymmetric steady convective flows were induced when the magnitude of the radial component of the magnetic force (f(mR)) was 1.0 and 5.0 times that of the gravitational force at the vessel sidewall; e.g., the hot air was concentrated at the vessel center and the cold air was driven to the vicinity of the vessel sidewall. This flow pattern was similar to the case of water (a diamagnetic substance), although the axisymmetric arrangements of hot and cold water were the reverse of the present convection of air. When f(mR) was 0.5 times that of the gravitational force, the axisymmetric flows appeared only in the vicinity of the vessel sidewall. Unsteady convective rolls simultaneously occurred in the vessel center, and they repeatedly combined and separated from each other. When f(mR) was 0.1 times that of the gravitational force, there were barely any axisymmetric flows in the close vicinity of the vessel sidewall, while the initial convective flows remained in most other parts of the vessel. Thus, we varied the magnitude of f(mR) and clarified the transitional processes of isothermal and velocity distributions of magnetothermal convection. We discuss those convective flows with the magnitude and direction of f(mR).