The temperature and time dependence of exchange bias for as-deposited Ni81Fe19-NiO films is studied. Using various cooling and measurement protocols, different contributions to the exchange anisotropy are separated. Depending on the cooling procedure, a strong increase or a controlled reversal of sign of exchange bias field is achieved at lower temperatures far away from the antiferromagnetic blocking temperature. The behavior is explained in terms of antiferromagnetic grain instability and the influence of the interfacial spin structure, the latter freezing at very low temperatures.