Abstract This paper presents an investigation of the thermoelastic problem of two offset parallel cracks in an infinite orthotropic plane. It is assumed that the orthotropy is attributed to the unidirectional fiber-reinforcement and the insulated cracks are aligned along the fiber direction disturbing a steady-state uniform heat flow. Based on the use of Fourier integral transform method, formulation of the current crack problem is reduced to two sets of Cauchy-type singular integral equations for heat conduction and thermal stress analyses, which are solved via the expansion-collocation technique. The thermally-induced singular interactions between the two neighboring cracks are elaborated by defining and evaluating the heat-flux intensity factors and the thermal-stress intensity factors. Numerical results include the variations of such near-tip field intensity factors for various combinations of material and geometric parameters of the cracked orthotropic medium. In particular, the effect of degree of thermoelastic orthotropy on the strength of heat flux and thermal stress singularities is addressed by varying the fiber volume fraction of fibrous composites.