Is there a Shar’i prohibition against a woman sitting in a man's place immediately after he stands up from the same seat while it is still warm, and what is its evidence, and does this ruling also apply to a man?

It was narrated that Ibn Umar (may Allah be pleased with them both) disliked a man sitting in a woman's place until it cooled down, as a way of blocking the means (to sin) and averting temptation. There is no evidence for this from the Qur'an or Sunnah. So, whoever adopts it, it is good; and whoever leaves it, there is no blame on him, as long as he does not intentionally stir up temptation.