Since nobody else has replied, I will give it a shot. I'm not at all familiar with the way Simulation handles this (I mostly use ANSYS) and I have no experience with thermal analyses, so I won't be much help.
On your first question, are you changing the temperature so much that the CTE changes significantly? If so, you may have to pick an average value for the CTE. It seems to me that would probably be adequate, if you can't figure out how to tell the system to use a temperature dependant curve.
On the second question, I don't believe that the cooling rate will affect the residual stress, unless you are cooling at really extreme rates. I think you would have to cool it so fast that the surface would shrink so much faster than the interior that you would yield the material just under the surface. I doubt that any normal cooling process would result in that situation.
On my first question, yes. The CTE of my selected material will change significantly with the temperature. Can you tell me how to tell the system to use the temperature dependant curve?
Looking forwards for your recommendation. Thanks a lot.