The olivine Mn2SiS4 is antiferromagnetic (AF) up to 83 K, behaves as a weak ferromagnet (WF) from 83 to 86 K, and becomes paramagnetic (P) at higher temperatures. Its counterpart Fe2GeS4 undergoes similar transitions in a reversed order: WF up to 69 K, AF up to 144 K and then P. These transitions are characterized by susceptibility measurements and investigated by high resolution specific heat experiments. The transition to the paramagnetic state is of the critical type and belongs to the universality class of the Heisenberg model for Mn2SiS4 and the 3D Ising model for Fe2GeS4. The WF/AF or AF/WF transition is of first order with a latent heat ΔH = 0.09 J/mol for Mn2SiS4 and ΔH = 105 J/mol for Fe2GeS4. The lattice is found to be stiffer for the Mn thiosilicate than for the Fe thiogermanate.