Final answer:
A relatively cool and expanded star larger than the Sun is a supergiant. These stars become larger and more luminous but have cooler surfaces as they evolve from the main-sequence phase before ending as white dwarfs.
Step-by-step explanation:
A relatively cool star that has expanded to more than 7000 times as large as our sun is known as a supergiant. These stars experience an evolutionary phase where, although their cores are contracting, their outer layers are expanding, making the star both more luminous and cooler compared to its previous state as a main-sequence star. Such a star can be seen in the red supergiant Betelgeuse, which has a much larger radius and lower average density but a cooler surface and a much hotter core than the Sun.
When a low to intermediate-mass star like our Sun ends its main-sequence phase, it goes through a red giant phase before ending its life as a white dwarf. During this time, it expands, cools, and becomes more luminous. This is a part of the stellar evolution that takes place after a star has exhausted its hydrogen fuel in the core and begins fusing hydrogen in a shell around the core.