Magnetic bistability between vortex and single domain states in nanostructures are of great interest from both fundamental and technological perspectives. In soft magnetic nanostructures, the transition from a uniform collinear magnetic state to a vortex state (or vice versa) induced by a magnetic field involves an energy barrier. If the thermal energy is large enough for overcoming this energy barrier, magnetic bistability with a hysteresis-free switching occurs between the two magnetic states. In this work, we tune this energy barrier by tailoring the composition of FePd alloys, which were deposited onto self-assembled particle arrays forming magnetic vortex structures on top of the particles. The bifurcation temperature, where a hysteresis-free transition occurs, was extracted from the temperature dependence of the annihilation and nucleation field which increases almost linearly with Fe content of the magnetic alloy. This study provides insights into the magnetization reversal process associated with magnetic bistability, which allows adjusting the bifurcation temperature range by the material properties of the nanosystem.