  Motivated by recent thermal conductivity measurements in the superconductor
CeCoIn5, we theoretically examine a possible staggered spin-triplet
superconducting order to be induced by the coupled spin-density-wave (SDW) and
d-wave superconducting (SC) orders in the high field and low temperature (HFLT)
SC phase peculiar to this material with strong paramagnetic pair-breaking
(PPB). It is shown that one type of the $\pi$-triplet order is consistent with
the thermal conductivity data and can naturally be incorporated in the picture
that the Q-phase is a consequence of the strong PPB effect inducing the SDW
order and the FFLO spatial modulation parallel to the applied magnetic field.
