The high-pressure form of solid water, ice III, is the equilibrium phase in contact with liquid water at pressures from about 2.0 - 3.5 kbar. Consequently, its properties are important in calculating the volume changes on freezing of subsurface oceans inside icy planetary bodies and the buoyancy of icy volcanic melts. The incompressibility (bulk modulus) of ice III as found by quantum mechanical simulations is much lower (<60%) than that of the other ice phases at neighbouring pressures and temperatures, but it is not known whether its thermal expansion is similarly "anomalous". We shall use HRPD to investigate metastable ice III (= ice IX, when proton ordered) by high-resolution neutron powder diffraction so as to determine both its thermal expansion and, from accurate structure refinements, the extent of proton ordering in its crystal structure.