Here's why:
* Copyright law protects original works of authorship, not general words or concepts. The word "hot" is a common, everyday word that exists in the public domain and cannot be copyrighted.
* Trademarks can protect brand names and logos, but not descriptive terms. While Paris Hilton has trademarked some of her phrases and brand elements, "hot" is too generic and descriptive to be a trademark.
It's important to note that Paris Hilton has become synonymous with "hotness" in popular culture, but that's due to her image and persona, not the legal protection of the word itself.