Because the helium fuel source will release more energy than hydrogen, the Sun's outer layers will swell, as well as leaking away some of its outer atmosphere to space. Since the Sun's fuel source will not have increased in proportion to its size, the blackbody power law indicates that the surface of the Sun will be cooler than it is now, and will become a cool, deep red. The Sun will have become a red giant. For very massive stars, this second core collapse would lead to a carbon main sequence, where carbon would fuse into even heavier elements, such as oxygen and nitrogen. The resulting dense, degenerate core is called a white dwarf, with a mass of something like the Sun compressed into a volume about that of the Earth's.
White dwarfs are initially extremely hot.
But since the white dwarf is supported by degenerate electrons, and has no nuclear fuel to speak of to create more heat, they have no alternative but to cool.