Question: how does cold and hot compress relieve pain?

David Bremner answered on 6 Mar 2025:

Applying Cold reduces the blood flow to any injured area, thus slowing the rate of inflammation which reduces the risk of swelling.
It also acts to numb the area similar to the effect of a local anesthetic, which slows down pain messages getting to the brain.

Applying heat acts in the reverse, opening up the blood vessels and getting more blood flow to the affected area to try to relax the muscles.