To reduce muscle soreness there seems to be a relationship between temperature and duration. But method also matters:
Ice baths 11-15 mins at 11-15°C
Ice packs leave the freezer between 0°C to -25°C, apply for 10-20 mins
Cryo-chambers can reach -140°C. For timing follow operator instruction
Too long or too cold and you risk burning your skin. Too little or not cold enough and you do not elicit the physiological changes that assist recovery.