We have analysed the onset of superconductivity in an Al mesoscopic disk, with a perpendicularly magnetized magnetic dot on the top. An insulating Si spacer layer between the Al disk and magnetic dot ensures that the interaction between them occurs only through the stray field of the magnetic dot. The superconducting T,(B) phase boundary is asymmetric with respect to the polarity of the applied magnetic field. The maximum critical temperature is achieved for a finite value of the perpendicular applied magnetic field, which is parallel to the magnetization of the magnetic dot. (C) 2004 Elsevier B.V. All rights reserved.