The problem of circular elastic inclusion with multiple interface cracks in an infinite dodecagonal two-dimensional symmetrical quasicrystal is studied under the action of a point heat source. Based on the holomorphic theory of complex function partition, the residue theorem, the generalized Liouville theorem, the Riemann-Schwarz analytic extension theorem and the singular principal part analysis method of complex stress function, the general complex potential solutions of temperature field, and the phonon field inside and outside the inclusion are obtained when the concentrated heat source acts on any point in the matrix. The closed form solutions of temperature field and phonon field thermal stress with one interface crack and two interface cracks are derived. The results are compared with the existing results, and the validity of the method is verified. Finally, the influence of inclusion radius, the heat source strength and crack angle on thermal stress and thermal stress intensity factor is discussed by numerical examples. The results show that the thermal stress of phonon field at the crack tip increases with the increase of heat source intensity. With the increase of crack angle and the increase of radius, the thermal stress intensity factor of phonon field at the crack tip increases and the change trend of thermal stress intensity factor is more obvious, and the higher the peak value is, that is, the increase of crack angle and inclusion radius promotes the crack propagation. These conclusions provide a scientific basis for the structural design and application of quasicrystal materials.