Why is the answer not d in the first PRS question?
A white dwarf is no longer contracting. It’s already contracted as much as it can, and is held up by degeneracy pressure rather than thermal pressure. It originally heated up by conversion of gravitational to thermal energy while it was contracting, but once the contraction has stopped, there’s no more conversion of energy. The star then just slowly radiates away the heat of its formation, and it cools.