A modified Monte Carlo method is used to study the dependence of exchange bias, induced by long-range ferromagnet/antiferromagnet interfacial dipolar interactions, on temperature after field cooling. Since sufficient nonzero surplus magnetization in the antiferromagnetic layer is preserved, a positive exchange bias field is yielded. Significantly, this exchange field increases with decreasing temperature and may level off at low temperatures. Then, the antiferromagnetic anisotropy constant, easy-axis direction with respect to the cooling-field direction, antiferromagnetic exchange constant, and antiferromagnetic layer thickness were modulated to study their roles in establishing the low-temperature plateau-like exchange bias field. A thick enough antiferromagnetic layer with the easy-axis direction aligning with the cooling field maximizes the plateau height with a large antiferromagnetic anisotropy constant, while a small antiferromagnetic exchange constant greatly widens the plateau, even from the exchange bias blocking temperature to the lowest temperature. On explicitly calculating the surplus magnetization values in the antiferromagnetic layer meanwhile the dipolar and Zeeman energies in the antiferromagnetic layer, it is found that the ferromagnet/antiferromagnet interfacial dipolar interactions are predominant at the descending branch of the loop to suppress the coercive field with decreasing temperature; in contrast, the magnetic field takes over the lead at the ascending branch and monotonically enhances the coercive field, at the same pace as the decrease in the coercive field at the descending branch. As a consequence, the loop retains a constant shift and becomes wider with decreasing temperature. The long-range noncontact exchange bias that is insensitive to temperature may be used to develop thermal-agitation-resistant spintronic devices with unidirectional anisotropy.