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 {i
t bosonic} holes, which is an effective system of the Bose-Hubbard model with strong repulsions. The bosonic electron operator $B_{rsigma}$ 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) $z_{rsigma}$ and a holon described by a hard-core-boson field $phi_r$ as $B_{rsigma}=phi^dag_r z_{rsigma}$. 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.
