Recently, the dependence of exchange bias (EB) on ferromagnetic layer thickness (t FM ) and temperature has become a matter of controversy, triggering renewed research efforts to decipher the key aspects of these intriguing phenomena. To demonstrate these anomalous dependences linked to the ferromagnetic spin structures, a modified Monte Carlo method is used on models of NiFe/antiferromagnet and Fe/antiferromagnet bilayers where a twisted configuration is favored along the film depth in the ferromagnetic layer during magnetization reversals. It is found that the EB field deviates from the reciprocal relation with t FM towards a lower value as t FM increases, and the maximum value of the EB field with temperature appears at 97 K for NiFe and 123 K for Fe, not the lowest temperature. The decrease in the EB field with t FM may also depend on the thickness of the antiferromagnetic layer and the twisted angle. The twisted configuration formed in a thick ferromagnetic layer encourages the propagation of domain walls through the ferromagnetic film to decrease the external switching field, leading to a suppressed EB. On the other hand, this twisted configuration simultaneously widens the domain walls and removes the unstable pinning points at relatively high temperatures. As a result, EB is recovered.