Abstract <p>A significant temperature gradient occurring in composites near interfaces between homogeneous components with essentially different thermal conductivity characteristics can degrade the performance of the materials. In view of this, it is important to predict local temperature fields at the interfaces between components in a composite. In this study, the problem of calculating the temperature field strength at the boundary of an inclusion in a matrix composite on the matrix side is solved. Using the generalized singular approximation, expressions for the operator of the concentration of the temperature field intensity on the surface of anisotropic inclusions in the form of highly oblate ellipsoids in the matrix composite are derived. These expressions show how the strength of the temperature field depends on the position of the point on the inclusion surface, the volume fraction of inclusions in the material, the orientation of the inclusion in relation to the direction of the intensity of the applied temperature field. This operator relates the fields on the inclusion surface on the matrix side to the average temperature field intensity in a composite sample. Using the derived expressions, model calculations are performed for a composite with an ED-20 polymer matrix and multilayer graphene inclusions. The absolute values of the temperature field intensity at points on the edges of inclusions on the matrix side are calculated at a fixed applied temperature field strength, different aspect ratios of the ellipsoids modeling the graphene inclusion shape, and different angles describing the mutual orientation of an inclusion and the applied field vector. It is shown that, in the case of graphene multilayer inclusions, the field strength on the polymer matrix side at points on their sharp edges can exceed the applied field by several orders of magnitude.</p>