I know that genital hpv virus is not viable agent but a kind of dna particle. however i wonder is it higher chance to live hpv virus in warm environment such as sauna?

Nobody really knows: Nobody knows how long HPV viruses survive on real-life inanimate surfaces. We vaccinate, and don't worry about objects transmitting such viruses unless the humans have such viruses and are intentionally getting viruses onto the objects. Read: https://www.canada.ca/en/public-health/services/laboratory-biosafety-biosecurity/pathogen-safety-data-sheets-risk-assessment/human-papillomavirus.html