Significant thermal stresses are introduced into the adhesive layers of a metal–composite bonded joint due to the large differences in coefficients of thermal expansion between the metal and composite adherends. In this study, theoretical analysis of shear and peel stresses in the adhesive layers of a double-lap metal–composite bonded joint was performed to evaluate the effects of thermal and mechanical loads on the stress distribution in the adhesive layer. The results obtained by the theoretical analysis and the finite element method were compared to validate the derived theoretical analysis. The effects of temperature change and adhesive thickness on the shear and peel stresses in the adhesive layer of the bonded joint, with and without external force, were examined theoretically. The results calculated for the conditions involving mechanical load application to the bonded joint and decreasing temperature indicate that the absolute value of shear and peel stresses peak at both ends of the adhesive layer and that the absolute value of the peak stresses increases with a thinner adhesive layer. When mechanical and thermal loads are simultaneously applied to a double-lap joint, shear and peel stresses synergistically increase at one end of the adhesive layer and decrease with offset at the other end.