The internal heat exchange between each phase and the local thermal equilibrium scenarios in multi-phase fibrous materials are considered in this paper. Based on the two-phase heat transfer model, a criterion is proposed to evaluate the local thermal equilibrium condition, using derived characteristic parameters. Furthermore, the local thermal equilibrium situations in isothermal/adiabatic boundary cases with two different heat sources (constant heat flux and constant temperature) are assessed as special transient cases to test the proposed criterion system, and the influence of such different cases on their local thermal equilibrium status are elucidated. In addition, it is demonstrated that even the convective boundary problems can be generally estimated using this approach. Finally, effects on local thermal equilibrium of the material properties (thermal conductivity, volumetric heat capacity of each phase, sample porosity, and pore hydraulic radius) are investigated, illustrated, and discussed in our study.