ATOMIC weight is what defines an element so no it is not dependent on temp.
Molecular weight is a determined thing too made up of the sum of the atomic weights of all the atoms in the molecule so - no it's not dependent on temp for a defined molecule.
The only possible dependents I could think of would be in a polymerisation, where the rate of reaction could be changed by increasing or decreasing the temperature, so, the resulting polymer could have a different molecular weight if the reaction temperatures were different. But I don't think that is what you were asking.