Specific heats (15-350 K) have been measured on 7 nm TiO2 anatase and rutile nanoparticles containing significant amounts of surface-adsorbed water. By successively reducing the water content without changing particle size, we observed two types of water behavior. The specific heat of bare 7 nm particles was estimated using the water specific heats. Contrary to previous literature reports, the bare small particle specific heats are the same as those of the bulk, within experimental error.