To calm down; for excitement, a scandal, anger, or fuss to die down — commonly used to mean the situation settles.
スキャンダルの影響が大きかったが、半年ほどでほとぼりが冷めた。
The scandal had a big impact, but it died down in about six months.
喧嘩の後は時間を置いて、ほとぼりが冷めてから話し合おう。
After a quarrel, let's wait until things calm down and then talk.
初めはファンも興奮していたが、数日でほとぼりが冷めた。
Fans were excited at first, but the excitement died down after a few days.