This phrase is an adjective used to describe someone who's demeanor is so cool that if you don't like them, there is something wrong with you; a literal description based on waking up at night, flipping your pillow, and the coolness making you feel so good you fall back to sleep.
Chris? Oh that dude is the shit! He's cooler than the other side of the pillow.
Ever notice how when you sleep with a pillow, that if your neck gets hot you can just flip your pillow over and the other side feels cooler than the side you were previously laying on?
Wow I really like that new tractor you got there, Bob! That thing is cooler than the other side of my pillow!