Hi mjames. I don't know the science of it, though 'warming' can have a calming effect… many have used this technique… (Gould, among others..) Whatever works for you is the key..
Also, deep breathing can be helpful. Also, being that stress is in the mind, sometimes deep breathing can make the moment feel Too serious, in which case, one could sing, in Long tones, one of the melodies, (or bass lines, for that matter) of the first piece to be played… This will also have you breathing deeper, yet with it not as the primary focus… Many have rituals before performing…
"superstition"? … Well I would argue that music itself is a kind of superstition of suspending the logic of 'the everyday'…

Cheers!
ps… sometimes the effect of warm water is not so lasting as, say, wearing fuzzy leather gloves from an hour before the performance starts…