In a joint of two dissimilar materials, stresses at the intersection of the edges and the interface are very high or singular for elastic material behavior. For most joint geometries and material combinations there is a type of r omega singularity. However, for some joint geometries and material combinations there is a type of r omega ln r singularity. In this article, the type of r omega ln r stress singularity will be treated by the Mellin transform method for a joint of two dissimilar materials under thermal loading. The emphasis is placed on the analytical description of the stress distribution near the singular point. The angular functions are given in a general form. They are different from those of the same joint under edge tractions. Two examples are presented to show the good agreement of the stresses calculated by the finite element method and from the analytical description for a finite joint; the unknown factors used to describe the stress distribution are also determined.