The problem specification is missing two important material constants: the Isotropic Secant Coefficient of Thermal Expansion for each sphere material.
Another important specification for a Thermal model that is missing from the specification is the thermal strain-free temperature or reference temperature of the components. If this structure was assembled with both spheres at 20C, then you get a different stress at the (0C, 10C) state than if the structure was assembled with both spheres at 0C.
The problem says the temperature of the large sphere is 0C. You have taken that to mean the entire body is at 0C. Your assumption makes the problem easy to solve because you can apply the Thermal Condition as you have done.
However, I would assume that 0C is just at the surface of the large sphere because that is a more physically realizable condition. In that case, you need to have the temperature gradient from the small sphere surface at 10C to the large sphere surface at 0C. One way to create that temperature distribution in the body of the large sphere is to solve a Steady State Thermal analysis and feed the solution of that into the setup cell of a Static Structural model.