Suppose stress-free, homogeneous but thermally anisotropic solid bodies (perhaps made of different materials) are joined together at a temperature \(\theta_ o\) along bounding surfaces which are pieces of planes. Under which conditions do the joints remain stress-free as the temperature changes? \textit{J. L. Ericksen} [J. Elasticity 13, 3-15 (1983)], addresses this problem in an important special case; here the author considers the question in general. The algebraic problems involved are delicate and the results are, almost of necessity, not exhaustive; however, a number of interesting classes of solutions are brought in evidence. The connections with questions of symmetry, stability and twinning are also discussed.