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The heat transfer problem in the 2-phase composite material containing metallic and elastic phases, subjected to quick temperature variations, is the aim of theoretical analysis. The full description of the composite behaviour starts from the formulation of governing equations at 2-scale levels: micro-and macro-, passes through specification of the internal structure of the composite and finishes by numerical solution of the heat transfer problem through the considered material sample. The most important in the analysis are thermo-mechanical properties of the composite components creating the material. The big difference of the both phases properties (mismatch) can create additional difficulty in the exact thermal description of the composite. It is necessary also to specify by scanning electron microscopy (SEM) observations a real material internal structure, which includes: grain shapes and matrix, to create of the proper size of the Representative Volume Element (RVE) for numerical calculations.In the numerical example we analyse cermet, i.e. the composite build up of metallic matrix (cobalt) and tungsten carbide elastic grains, which exhibits high brittleness. Heat transfer across this very complex material causes heat flux concentrations in the metallic
