To study the mechanical laws governing the form of multicellular organisms, we examine the morphology of adhering vesicle doublets as the simplest model system. We monitor the morphological transformations of doublets induced by changes of adhesion strength and volume/area ratio, which are controlled by intermembrane interactions and thermal area expansion, respectively. When we increase the temperature in the weak adhesion regime, a dumbbell flat-contact doublet is transformed to a parallel-prolate doublet, whereas in the strong adhesion regime, heating transforms the dumbbell flat-contact doublet into a spherical sigmoid-contact doublet. We reproduce the observed doublet morphologies by numerically minimizing the total energy, including the contact-potential adhesion term as well as the surface and bending terms, using the Surface Evolver package. From the reproduced morphologies, we extract the adhesion strength, the surface tension, and the volume/area ratio of the vesicles, which reveals the detailed mechanisms of the morphological transitions in doublets.