We propose a new technique, ''three terminal arbitrary heating method'' for the thermal diffusivity alpha measurement which at the same time enables one to determine the contact thermal resistance R(c) between the sample and holder. By this method, the error in alpha due to R(c), which becomes progressively consequential at lower temperatures, can be eliminated. The method has been applied to YBa2Cu3O7-delta oxide superconductors and the specific heat C has been accurately determined between 15 to 200K by use of the relation C-kappa/alpha, where kappa is the thermal conductivity quasi-simultaneously measured with alpha.