system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why does putting cold fingers or toes in comfortably warm water cause a burning sensation?
gpt
A combination of two things working together:

1. Your skin doesn't sense the actual temperature of things, you sense the *rate* that heat is entering or leaving the skin.
2. The rate of heat transfer gets faster the bigger the temperature difference between two things. 

When your skin surface is cold, the "warm" water is hotter by comparison than it usually is. When you put freezing hands in warm water, heat starts entering your skin at a fast rate, a rate that tells your brain "water 50 degrees warmer than skin temperature". Your skin temp is usually body temperature, so your brain goes "oh shit, nearly-boiling water!" Except your skin was way colder than usual and the water was only normally-warm. But your temp sensors can only tell temperature *differences*, so there's no way to tell the difference. 

Extra info:

Think about how a metal railing outside in the winter feels colder than something wood like a tree, even they're both the exact same temperature. That only happens because metal is a way better heat-conductor than wood. So cold metal can draw heat from your skin's surface faster than cold wood of the same temperature can, so you feel the metal as being "colder" because the *rate* of heat loss is faster..

Another example in case you don't live somewhere with cold winters: wooden toilet seats vs plastic toilet seats. The wood ones feel warmer, right? Both are the same room temp, but again wood is a poor heat conductor while the plastic seat draws your heat away faster.