In material contact problems, localized subsurface temperature change can lead to changes in the stress gradient, which significantly affect the contact performance and service life of the material. In practical engineering materials, regions of localized temperature change often exhibit irregular shapes with smooth curved edges or sharp corners, pose substantial challenges for analytical solutions. This paper presents an algorithm based on singular integral equation of the first kind to solve the frictionless contact of a half-plane with a localized subdomain, subjected to temperature change, with a rigid circular punch. Compared to the finite element method, this work only requires discretization of the contact region, thereby significantly enhancing computational efficiency. By comparing with the classical Hertzian solution, the noted effect of localized subsurface temperature change on the contact region is verified. Taking a half plane with rectangular or circular temperature rise regions in contact with a rigid punch as examples, the computational results of current method are compared with those of the finite element method, which further demonstrate the accuracy and efficiency of the algorithm.