Vibrational spectra of three-component BaTiO3/SrTiO3/CaTiO3 short-period superlattices grown by pulsed laser deposition with atomic-layer control have been investigated by ultraviolet Raman spectroscopy. Monitoring the intensity of the first-order phonon peaks in Raman spectra as a function of temperature allowed the determination of the ferroelectric phase transition temperature Tc. Raman spectra indicate that all superlattices remain in the tetragonal ferroelectric phase with out-of-plane polarization in the entire temperature range below Tc. The dependence of Tc on the relative thicknesses of ferroelectric (BaTiO3) to nonferroelectric materials (SrTiO3 and CaTiO3) has been studied. The highest Tc was found in superlattices having the largest relative amount of BaTiO3, provided that the superlattice maintains its coherency with the substrate. Strain relaxation leads to a significant decrease in the ferroelectric phase transition temperature.