  We study numerically the temperature dependencies of specific heat,
susceptibility, penetration depth, and thermal conductivity of a coupled
$(d_{x^2-y^2}+is)$-wave Bardeen-Cooper-Schreiffer superconductor in the
presence of a weak s-wave component (1) on square lattice and (2) on a lattice
with orthorhombic distorsion. As the temperature is lowered past the critical
temperature $T_c$, a less ordered superconducting phase is created in
$d_{x^2-y^2}$ wave, which changes to a more ordered phase in $(d_{x^2-y^2}+is)$
wave at $T_{c1}$. This manifests in two second-order phase transitions. The two
phase transitions are identified by two jumps in specific heat at $T_c$ and
$T_{c1}$. The temperature dependencies of the superconducting observables
exhibit a change from power-law to exponential behavior as temperature is
lowered below $T_{c1}$ and confirm the new phase transition.
