Having absolutely nothing to do with me, the expression, "cooler than the other side of the pillow" has crept into popular culture. Apparently on ESPN SportCenter, Stuart Scott is fond of saying someone is "cooler than the other side of the pillow." This is a nice reference, although I have to say, it's not as popular as say, "Cool beans, dude" or "Coolio" or the ubiquitous "Cooler than an ice cube that has been in the freezer with all the other ice cubes and frozen foods and that ice pack you use every now & then when you sprain an ankle." Without dating myself (which, btw, is a physical impossibility considering how much dating can cost these days), Cool Pillows goes back many years before ESPN, let alone Stuart Scott.
Just to show I'm not making this all up. Here's some other references to other types of cool pillows, on the web. I don't know why I'm linking to some of these, even though they are products and you might buy them. (Mental note: talk to these companies for affiliate marketing remuneration.)