Cooler's History
Background
Like the rest of his family, Cooler is shown to be involved in the Frieza Force, although he does not appear to work closely with his family. He also leads his own squadron of warriors as a planet subjugator for the Frieza Force. According to an issue of Shonen Jump, Cooler has control of at least 256 planets, as his henchman, Dore is stated as hailing from planet Coola No. 256.
In Age 737, while Frieza destroyed Planet Vegeta, the home planet of the Saiyans, a newly-born Kakarot was being sent to subjugate Earth. Seeing that Goku had escaped the explosion, Cooler's henchmen made plans to shoot the space-pod down. Cooler unexpectedly delayed the order, lamenting that his brother was still far too soft to allow a child's escape and that Frieza's conceit would delay the annihilation of the Saiyan race and jeopardize his family's absolute control over the galaxy. He and his squad were also tasked with the subjugation of seven planets by the end of that day.
Cooler always had a sibling rivalry with Frieza and even went as far as to admit that if Goku had not killed Frieza, he himself would have tried to kill him. At some point, Cooler found the means to gain a clear advantage over his younger brother: he transformed into a Fourth Transformation, with power surpassing even his younger brother's full power at the time.
Cooler's Revenge
Roughly 27 years after the genocide of the Saiyans, Cooler is given the word that his brother had been killed by a Saiyan. Initially skeptical, he soon comes to believe it, and heads to Earth to restore his family's honor (he makes the point that he is not doing this to avenge Frieza. In the FUNimation dub, he also bitterly states that part of the reason Frieza got beaten was that their father, King Cold, "spoiled Frieza rotten"). Upon arriving, he makes his henchmen encounter a Saiyan, who of course is Goku. As Goku was unaware of Frieza having a brother, he mistakes Cooler for Frieza and is shocked at the apparent survival of "Frieza". Cooler wounds Goku in a blast intended for Gohan but loses sight of his quarry after Goku is washed down a waterfall. This encounter leads Cooler to suspect that Goku did, in fact, kill Frieza, since Goku had thrown a powerful ki blast from a very compromising position after he had been hit by Cooler's eye beams. Not content to blow up the planet & being too proud and eager to smite the one who injured his family name, Cooler goes to some lengths to have him tracked down.
With Dore and Neiz killed by Piccolo and Salza almost defeated by him, Cooler finally enters the battle himself, with Piccolo expressing shock, believing him to be Frieza and stating that he should be dead. Cooler punctures a hole through Piccolo and has Salza go after Gohan. Goku, revived by consuming a Senzu Bean, encounters Cooler, learning he is Frieza's brother as Cooler demonstrates how much mercy he lacks, by dropping Piccolo, (pretending to let Piccolo go for Goku to rescue him) and then blasting Piccolo before Goku could catch him. Goku, enraged, condemns Cooler as ruthless as his brother before beginning his battle with Cooler. Initially, he and Cooler are a fairly even match; Cooler then understands how Goku gave his brother trouble. He soon reveals to Goku that Frieza was always trying to beat him at everything and that he would have killed him sooner had it not been for his father; this implies that Cooler was planning on killing Frieza before his confrontation with Goku, and desired to kill Goku mostly for robbing him of his chance of doing so, rather than family matters. Cooler soon tells Goku of his ability to transform once more than Frieza and shows him his ultimate transformation (in Funimation's dub).
Cooler now easily overpowers Goku in this form, and keeps to his word to make sure the Saiyan suffers for bringing shame upon his family's legacy, by attacking Goku with back-breaking techniques, almost bringing Goku to death, until at length he grows tired of the fight and feels Frieza had further shamed his family by dying at Goku's hand. As he makes plans to destroy the planet, Goku's rage transcends, transforming him into a Super Saiyan. Off-guard and arrogant, Cooler is overpowered by the Saiyan; he realizes how Frieza lost to Goku and laughs crazily at it. Finally becoming desperate, he gathers enough energy to form a Supernova (the same attack Frieza used to destroy Planet Vegeta) to obliterate the Super Saiyan and Earth. However, with a powerful Super Kamehameha, Goku is able to offset his attack and send Cooler hurling into the Sun (In the Funimation dub, when Cooler first notices the Sun while being knocked back by Goku's Super Kamehameha, he considers destroying the Sun with the intention of causing the Earth and the surrounding Solar System to freeze in darkness, but stops when he realizes that he is heading right towards it). Cooler realized that Goku was the Saiyan child he had allowed escaping nearly three decades ago and that in scolding his brother and not lifting a finger, he had been far too soft himself. Cooler is then incinerated in the Sun.
The Return of Cooler
Cooler's remains float around in space and eventually fuse with the Big Gete Star, a giant machine. The Big Gete Star revives Cooler by finally fusing with his brain, causing him to fuse with it into Meta-Cooler Core. Meta-Cooler Core set a course for New Namek, intent on draining the planet and using the Namekians as fuel for the star. Dende, learning of this horrible news, calls to Earth's warriors for help; Goku, Gohan, and Piccolo, as well as Krillin, Master Roshi, Oolong, and Yajirobe, travel to New Namek, ready to assist its people.
Meta-Cooler appears before the Dragon Team. Stronger than ever, he is able to face Goku and Vegeta. The two Super Saiyans have trouble defeating Meta-Cooler, but eventually do so. However they discover that it was not Cooler himself but a remote controlled duplicate. An army of Meta-Coolers emerge to attack and overwhelm the duo, who are taken into the star.
Goku and Vegeta encounter the remains of the actual Cooler, an obscene and grinning head split with one remaining eye, strung up by wires and sheets of metal and integrated into the Big Gete Star's main computer. After a conflict with Meta-Cooler Core's Battle Form, what is left of Cooler is destroyed by Goku.