[en] Epitaxial Nb/FePt thin film bilayers were prepared by pulsed laser deposition under UHV conditions. With the magnetic moments of the FePt grains aligned perpendicular to the film plane, the stray field between the individual grains acts already on the superconductor in the field-free case. Under application of an external magnetic field, the stray field can be compensated for, accompanied by an observable increase of the transition temperature. This field compensation effect can be tuned by changing the density of the magnetic grains or the magnitude of the stray field. The magnitude of the already reported shifts in the transition temperature are in the range of 40 mK when fields of 2 mT are applied. Using FePt hard magnetic materials an enhanced effect of stray field compensation was observed when 0.25 T of applied field raises T_C by about 0.5 K. The extension of the superconductive phase in the μ₀H(T) phase diagram of the heterostructures was investigated. An asymmetric behavior of the phase boundary with respect to the polarity of the applied magnetic field was observed, which can be controlled by varying the FePt layer thickness