No you wouldn't want to run your hands under hot water or even use hot water on your face-ever, its very drying and aging.
Here is a picture I actually found of what to do, it doesnt show their 'Method of Use' as exactly as I described, you apply the product in your palms, just a few pumps, and place your hands together so your right thumb is near the bottom of your left palm, and then gently press together for a few seconds, lift your hand off, turn your top hand (your right hand still) so that your thumb comes to the middle of your left index finger. This is just warming the product up.
Do not use a lot of friction, when applying to the face, apply gently, smooth it over your face and always smooth outwards.
I looked up Clarins Method and came up with mostly photos of products and a few boutiques, Clarins is huge in Asia and France, and apparently, the #1 Leader and Best-Seller of Cosmetics in Europe.
Anyway, look at the first photo, which says 'Method of Use' for a general idea, except not on your fingertips, your palms.
Photo source is dailymail.co.uk for the facial photo, other is uk.boutique.clarins.com