We demonstrate the dramatic effect of film thickness on the ferroelectric phase transition temperature Tc in strained BaTiO3 films grown on SrTiO3 substrates. Using variable-temperature ultraviolet Raman spectroscopy enables measuring Tc in films as thin as 1.6 nm, and a film thickness variation from 1.6 to 10 nm leads to Tc tuning from 70 to about 925 K. Raman data are consistent with synchrotron x-ray scattering results, which indicate the presence of 180 degrees domains below Tc, and thermodynamic phase-field model calculations of Tc as a function of thickness.