By using a gauge transformation of the vector potential that accounts for the superconducting/vacuum boundary condition, we solve the linear and nonlinear Ginzburg-Landau equations to calculate the phase diagram of the hybrid superconducting/ferromagnetic nanostructure formed by a superconducting microsquare with a magnetic disk on top. Close to the normal/superconducting phase boundary [T-c(H)] we observe that the competition between the applied magnetic field and the inhomogeneous field of the disk strongly affects the vortex nucleation. As a consequence, different symmetry constraints are imposed on the vortex patterns at T-c(H), leading to the exclusion of some vorticity values allowed in the no-dot case. The dot also influences the evolution with temperature of the vortex states deep in the superconducting phase, giving rise to instability processes that differ from those previously found in individual microsuperconductors and that may involve the spontaneous generation of additional vortices. Besides, the dot also forces the vortex matter in this hybrid nanostructure to behave similarly to the case of an individual microdisk in some regions of the phase diagram.