In this paper, a heat conduction equation and a dynamic thermoelastic equation are briefly deduced and established based on Continuum Mechanics.

First, an qualitative discussion is emphatically centered around the couple term and the dynamic term of the equation by means of the dimensional analysis and by considering the combination of the characteristics of the materials and of the thermal load effected on the nuclear power station pump under study.

Second, formulations of the FEM for non-coupled heated equations and quasi-static thermoelastic equations are derived in this paper.

Third, a half space thermal shock problem is used as a computational example in the highlighted research on the varying behavior of the dynamic thermal stress on the temperature slope. The conclusion of the paper provides reliable justification for applying the numerical method.

Finally, the distribution and variety of the temperature field, the thermal stress field and the thermal deformation field at various transient moments on the pump are given.

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