Cooling crust before filling purpose?

When you're making an uncooked pie with a docked and blind baked pie crust base (such as the fresh strawberry pie I'm making or French Silk), what is the purpose of allowing the crust to cool completely before filling and refrigerating to set?
Does it make a difference in the finished product if the crust is still warm when you add cool/room temperature filling, or if the crust is cool and you add filling that is still warm?