The hysteresis loop shift H E of sub-100-nm ferromagnetic-FM-antiferromagnetic AFM nanostructures is found to be strongly influenced by thermal activation effects. These effects, which tend to reduce H E , are more pronounced in the nanostructures than in continuous films with the same composition, particularly for thin AFM layers. In addition, the reduced dimensions of the nanostructures also impose spatial constraints to the AFM domain size, particularly for thick AFM layers. This favors an enhancement of H E. Due to the interplay between these two competing effects, the loop shift in the dots can be either larger or smaller than in the continuous films with the same composition, depending on both the AFM thickness and temperature. A temperature-AFM thickness phase diagram, separating the conditions resulting in larger or smaller H E in the nanostructures with respect to continuous film is derived.