Here is a goal: how to thicken a milkshake

Which way makes more sense to accomplish this goal?

pick from the following.
[I] once everything is blended, stick the blender top (not the motor) into the oven for 1-2 hours and then re-blend.
[II] once everything is blended, stick the blender top (not the motor) into the freezer for 1-2 hours and then re-blend.
[II]