The critical behavior of the paramagnetic to antiferromagnetic transition in RMnO 3 (R = Sm, Tb, Dy, Ho, Er, Tm, Yb, Lu, Y) has been studied with an ac photopyroelectric calorimeter, which gives simultaneously the thermal diffusivity and specific heat as a function of temperature with high resolution around the Néel temperature. RMnO 3 (R = Sm, Tb, Dy) has an orthorhombic perovskite structure, whereas the other manganites are hexagonal, thus revealing a strong thermal anisotropy. SmMnO 3 with an Type-A antiferromagnetic ordering exhibits a 3D-XY critical behavior, which could be attributed to the peculiar site anisotropy of Sm 3+ and the exchange interaction between Mn 3+ and Sm 3+ ions. The sinusoidal spin ordering in TbMnO 3 and DyMnO 3 can be phenomenologically described by the 3D-Heisenberg model. Finally, the hexagonal manganites RMnO 3 (R = Ho, Er, Tm, Yb, Lu, Y) are close to the 3D-Heisenberg universality class, ruling out the chiral models predicted by the renormalization group theory.