Joints feeling better is easy to believe, it suppresses inflammation after all, there's no contradiction with what I said. The research is on muscle adaptation. You want a certain degree of inflammation for the muscle to respond to training. Some have even theorized that increasing inflammation through arachidonic acid supps should increase muscle growth - William Llewellyn, who wrote the Anabolics books, patented this fatty acid for this purpose. NSAIDs also reduce muscle adaptation and hypetrophy. Yet research in the elderly showed that ibuprofen apparently increased hypertrophy. Why? It's likely the ibuprofen allowed these oldies to actually exercise, so the net effect ended up being a positive, even if it suppressed muscle growth to a degree.
Almost all athletes use NSAIDs perodically and the net effect is often positive, even if the per se effect of the drug hampers adaptation.
Check it out, a blog post on it, better format for the average reader than just the actual study.
https://suppversity.blogspot.com/2015/07/using-ice-cold-water-immersion-after.html?m=1
This is it right here. And also explains that NSAIDS actually helps with hypertrophy when you're old whereas when you're young it hinders it because it mutes the inflammation process necessary as a result of training. It helps old people just exactly as Van B said. Not because it mutes the inflammation process per se but because it just allows them to train.
It's heat that is best after training. It keeps the blood vessels dilated improving blood circulation and also relaxes the muscle. It also promotes some positive hormonal action which I can't remember the specifics.
Cold will definitely help with joint pain because it reduces inflammation just like when you ice an injury. But inflammation is needed for healing. Your body swells for a reason. Back in the late 90s I use to do prolotherapy which required multiple injections, about six all at once, where they inject a fluid in the tendons all across the joint. This was done to promote inflammation. Tendons don't get the blood supply like muscles do so the idea was to irritate it and cause inflammation to force the body to get circulation into that area. It worked. Can get it done here in Hawaii. It's also done by a real medical doctor.