Why antipyretics do not bring the body-temperature below normal?
Antipyretics doesn't work by reducing the body temperature but blocking pathways that make it higher.

For paracetamol/acetaminophen the mechanisms implied are not currently completely clear (as reported on Wikipedia or on Katzung's "Basic &amp; Clinical Pharmacology").

For the most common NSAIDs (aspirin, ibuprofen, naproxen, ...) the mechanisms instead are more clear as they block some enzymes that are involved in production on inflammatory molecules (enzymes COX1 and COX2 that are implied in the arachidonic acid pathway as said on this article).

When these inflammatory molecules rise concentration in blood they can get to the hypothalamus so it will set the body temperature at an higher level; when these signals stop coming (inflammation stops or no more molecules are produced because of drug's block) the hypothalamus sets the temperature to the normal range.

More infos about hypothalamic temperature set point.