Time-of-flight, neutron powder diffraction to 1000 degrees C provides precise octahedral site occupancies and intersite distribution coefficients for MnMgSiO4 and MnFeSiO4 olivines. Intersite exchange occurs in minutes down to 500 degrees C. Equilibrium distribution coefficients show that manganese ordering into the larger octahedral site decreases with increasing temperature. Exchange energies are 15.7 and 10.1 kilojoules per mole for magnesium-manganese and iron-manganese, respectively. Distribution coefficients deduced for FeMgSiO4 olivine suggest an exchange energy of 4.8 kilojoules per mole. Intersite exchange energies are consistent with diffusion coefficients in the order iron > magnesium > manganese. Geothermometry based on magnesium-manganese and iron-manganese exchange may be possible only for samples equilibrated below 500 degrees C.