In SOL106 (Standard Nastran Nonlinear), rigid elements follow small displacement theory. Additionally, the capability to use CTE on an RBE element is not available in SOL106.
In SOL400, when large displacement effects are requested, by default, the RBE elements follow large displacement theory. To force the RBE elements to use small displacement theory, use RIGID=LINEAR in the case control.
Also, in SOL400, the rigid elements can utilize a CTE defined on the RBE elements if a delta-t loading is defined.