Heat capacity and anisotropic thermal expansion was measured for Fe1.06Te and FeTe0.5Se0.5 single crystals. Previously reported phase transitions are clearly seen in both measurements. In both cases the thermal expansion is anisotropic. The uniaxial pressure derivatives of the superconducting transition temperature in FeTe0.5Se0.5 inferred from the Ehrenfest relation have opposite signs for in-plane and c-axis pressures. Whereas the Gruneisen parameters for both materials are similar and only weakly temperature-dependent above ~ 80 K, at low temperatures (in the magnetically ordered phase) the magnetic contribution to the Gruneisen parameter in Fe1.06Te is significantly larger than electron and phonon contributions combined.