Molecular solids like sodium superoxide NaO2 possess relatively simple crystal structures, yet their magnetism is surprisingly complex. This is presumably due to the interplay of spin, orbital and lattice degrees of freedom, which leads to intriguing effects related to reorientation of O2- molecular p orbitals. In such cases the cooling procedure leading to the magnetic ground state may be of high relevance. In our previous muSR studies of NaO2, we have discovered an intriguing magnetic phase below 3 K induced by an applied magnetic field of the order of only 100 G. Two different experiments that have been performed so far indicate a possible cooling-dependence of this effect. Here we propose to carry on the muSR investigation of the field-induced phase after various controlled cooling protocols. We expect that these measurements will finally unveil the mechanism of the observed effect.