Why when attempting to lower a person's body temperature in response to hyperthermia one should avoid treatments that induce shivering or vasoconstriction?

Because Shivering would make the body generate heat as a form of defense mechanism and  Vasoconstriction would reduce our body's ability to release the heat from our skin surface.

When we intended to lower another person's body temperature, both shivering and vasoconstriction would actually prevent us from doing so since they both would bring the body temperature come back up as we try to cool it down.