Which plays a better role in calming down inflammation: Warm water or cold water?

What kind of inflammation are you dealing with? Different organs have different treatments.

Generally cold is for swelling and heat is for pain, muscle strain.
Yes, as @WestRiverrat points out, what are we talkin’ about here?
Different applications apply to different conditions. You don’t want to run hot water over a severed artery. lol

Cold for swelling, warm for relaxing the muscle.

I din’t understand the drinking question. If you have a bad sore throat, really bad, feels like razor blades when you swallow, then ice water or popcicles are the way to go. It will numb the area a little and calm inflammation. That type of sore throat is usually from strep or mono. If it is a sore throat that bothers you, but not really when swallowing, which is usually the beginning of a cold, room temp is just fine, and then when it switches to no sore throat and a bunch of congestion, warm to hot liquids are usually the most comforting.

@WestRiverrat I guess general inflammation. Kind of the same that one would get from drinking too much bad acidic drinks like soda pops over long periods of time…

Drink what is comfortable. What works on muscle injuries generally does not work on intestinal inflammation. Next time you visit your health care professional, ask there.

@pleiades water at any temp is great for generalized inflammation. Usually the type of inflammation caused by a sugary diet is high acidity problem. Generally speaking you want to eat and drink things that are more alkaline to balance out the system but flushing it with citrus water is a great start… But aren’t those acidic? Predigestion yes the digestive ash they produce is alkaline because of the interaction of the gastric acids. Fish and fish oil a lot of spices turmeric is hugely popular for reducing inflammation as well as tons of other benefits… Fiberous diets also help nuts, berries, whole grains and seeds.
For gastrointestinal problems aloe juice is great.