  A linear system of differential equations describing a joint motion of
thermo-elastic porous body and incompressible thermo-fluid occupying porous
space is considered. Although the problem is linear, it is very hard to tackle
due to the fact that its main differential equations involve non-smooth
oscillatory coefficients, both big and small, under the differentiation
operators. The rigorous justification is fulfilled for homogenization
procedures as the dimensionless size of the pores tends to zero, while the
porous body is geometrically periodic. As the results, we derive Biot's like
system of equations of thermo-poroelasticity, system of equations of
thermo-viscoelasticity, or system of non-isotropic Lam\'{e}'s equations
depending on ratios between physical parameters and geometry of porous space.
The proofs are based on Nguetseng's two-scale convergence method of
homogenization in periodic structures
