  We study the three-dimensional bosonic t-J model, i.e., the t-J model of
"bosonic electrons", at finite temperatures. This model describes the $s={1
\over 2}$ Heisenberg spin model with the anisotropic exchange coupling
$J_{\bot}=-\alpha J_z$ and doped {\it bosonic} holes, which is an effective
system of the Bose-Hubbard model with strong repulsions. The bosonic "electron"
operator $B_{r\sigma}$ at the site $r$ with a two-component (pseudo-)spin
$\sigma (=1,2)$ is treated as a hard-core boson operator, and represented by a
composite of two slave particles; a "spinon" described by a Schwinger boson
(CP$^1$ boson) $z_{r\sigma}$ and a "holon" described by a hard-core-boson field
$\phi_r$ as $B_{r\sigma}=\phi^\dag_r z_{r\sigma}$. By means of Monte Carlo
simulations, we study its finite-temperature phase structure including the
$\alpha$ dependence, the possible phenomena like appearance of checkerboard
long-range order, super-counterflow, superfluid, and phase separation, etc. The
obtained results may be taken as predictions about experiments of two-component
cold bosonic atoms in the cubic optical lattice.
