The benefit of magnetoconvection for transformer cooling by ferrofluid is numerically studied. A code combining spectral and finite-element methods is applied on a solenoid system. Magnetostatic, Navier-Stokes, and energy equations are solved simultaneously. A vegetable oil seeded with magnetite nanoparticles at a volume fraction of 10% is considered. The magnetization of the ferrofluid is a function of temperature through an approximation of the classical Langevin's law. Magnetic and temperature fields are used to update the magnetic action, modeled by the Kelvin force, on the ferrofluid momentum at each time step. Numerical results for regular oil are consistent with experimental temperature data obtained for pure vegetable oil cooling. Numerical results for ferrofluid show that the magnetoconvection modifies the flow convection pattern and speed. The temperature increase in the coil is consequently reduced by about 9.4% with ferrofluid cooling.