We performed spin-polarized scanning tunneling spectroscopy on biatomic-layer-high Co nanoislands grown on Cu(111) in magnetic fields oriented normal to the sample surface, with Fe-coated W tips. Increasing the temperature from 10 to 30 K, we observe a reduced slope of the differential conductance around zero field. A quantitative analysis of the field- and temperature-dependent differential conductance data in the framework of superparamagnetism as described by a Langevin function gives an excellent description of the experimental results. The analysis suggests that a Fe nano-apex at the W tip, which is composed of 220-300 Fe atoms, determines the magnetic response of the tip.