We establish universal behaviour in the temperature dependencies of some observables in (s + id)-wave BCS superconductivity in the presence of a weak s wave. We find also a second second-order phase transition. As temperature is lowered past the usual critical temperature , a less ordered superconducting phase is created in the d wave, which changes to a more ordered phase in a (s + id) wave at . The presence of two phase transitions is manifested by the two jumps in the specific heat at and . The temperature dependencies of the susceptibility, penetration depth, and thermal conductivity also confirm the existence of the new phase transition.