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The problem of a Griffith crack embedded in an orthotropic strip is investigated under a combination of thermal and mechanical loadings. The extended thermal-medium crack model is used to address the effects of thermal conductivity of crack interior on the fracture parameters of concerns. Using the Fourier transform technique, the boundary-value problem is reduced to solving singular integral equations with Cauchy kernel. The closed-form solutions of temperature fields are determined. In solving the elastic fields, the Lobatto–Chebyshev integration formula is applied to discretize the obtained singular integral equations as a system of algebraic equations, which is solved by elaborating an algorithm. Numerical results are reported to illustrate the effects of the thermal conductivity inside crack and the thickness of orthotropic strip on the partial insulation coefficient, the thermal stress intensity factor, and the strain energy density factor. The crack initiation behavior is analyzed according to the normalized strain energy density factor. The observations reveal that the crack-tip thermoelastic fields in an orthotropic strip are dependent on the combined effects of the thermoelastic loadings, the physical and geometrical properties of the material and crack. Some comparisons with the existing works are offered to show the novelty and applicability of the obtained results.