Red Giants are actually hot stars, but their size and radiating surface area / energy density make any one point cooler, so it glows in the red. they radiate thousands of times more heat through their bigger surface volume than smaller stars.
A white dwarf is like having a tiny leak in a car tire, if the hole doesn't get any bigger, its only going to radiate away so much heat from its small size, and never more than that. the 'heat' behind it will stay there, and it will glow for billions of years.
A cold white dwarf is very unusual.