High stresses can occur in bonded dissimilar materials after a change in temperature in the vicinity of the intersection of the interface and the free edge. These stresses depend on the thermal expansion and on the elastic constants of the two materials. In bonded quarter planes the stresses near the intersection of the interface and the free edge can be described by the sum of one singular term and one regular term which is independent of the distance to the singular point. With the exception of the stress intensity factor of the singular term, all parameters can be calculated analytically. The stress intensity factor was evaluated numerically using the finite element method. Joints with different ratios of height to length and various material combinations were investigated. An empirical relationship between the stress intensity factor, the elastic constants and the ratios of height to length of the joint is given by exponential and polynomial equations.