The thermoelasticity problem of a coated polygonal hole subject to a point heat source is investigated herein. Based on conformal mapping, analytic continuation theorem, and alternation, temperature functions are obtained for any number of edges of a coated polygonal hole, while stress functions are obtained for a coated approximate triangle hole and a coated approximate square hole. Solutions of temperature contours and interfacial stresses agree well with the finite element results. Both the interfacial normal and shear stresses indicated an obvious concentration and a sudden jump across the corner of a coated polygonal layer, respectively. The present derived solutions can be considered as Green’s functions to study problems involving a crack interacting with a coated polygonal hole.