We have studied the temperature and thickness dependence of the exchange-induced unidirectional anisotropy field (H(s)) and coercive field (DELTA-H(c)) in Co/CoO bilayers using a Faraday balance. Results show that H(s) and DELTA-H(c) decrease monotonically with increasing temperature vanishing around T(crit) approximately 210 K, which is distinctly lower than the Neel temperature of bulk CoO (289 K). The unidirectional exchange anisotropy field shows the predicted proportionality to the inverse of the ferromagnetic layer thickness. We have observed that the temperature dependence of H(s) can be described by (1-T/T(crit))n, where n is a linear function of Co layer thickness.