The dependence of perpendicular exchange anisotropy on the thickness of the ferromagnetic (FM) layer in Mn-Ir / [Co/Pt]_n multilayers was investigated. The dependencies on temperature of saturation magnetization, M_s, in [Co / Pt]_n multilayers having Co and Pt layers of various thicknesses were examined. The rate of decrease of M_s against temperature was large for thin-Co (< 1 nm) or thick-Pt layers ( > 1 nm), which indicates that thermal fluctuations in magnetization were significant. The unidirectional anisotropy constant, J_K, was reduced with the decreasing thickness of the interfacial Co layer in contact with the Mn-Ir layer. This suggested that perpendicular exchange bias was degraded by thermal fluctuations in FM magnetization during thermal annealing. The dependencies of J_K on the thicknesses of the Pt layer and inner Co layer could be also described by the thermal fluctuations in the magnetization of the FM layer.