Introduced in Transformers: The Movie, Hot Rod is a young, brash, arrogant upstart of an Autobot, who thinks that he has all the answers. His actions are very immature, and he would rather spend his time partying than fighting for the greater good. It is implied in the movie that Hot Rod and Arcee have a budding romantic relationship, and that he sees Kup as a father figure. In Season 3, it's loosely implied that Springer may be Rodimus' best friend.
At the end of TFTM, it is revealed that Hot Rod is the legendary Autobot who would rise from their ranks to use the power of the Matrix to light their darkest hour. He unleashes the power of the Matrix to destroy Unicron, and begin leading Cybertron on a path towards a peaceful, golden age.
Hot Rod transforms into a magenta-and-orange Cybertronian sports car with yellow flame designs and an oversized yellow spoiler, much as his namesake might suggest.
After obtaining the Autobot Matrix of Leadership, Hot Rod becomes Rodimus Prime. As Rodimus Prime, Roddy is the insecure leader of the Autobots, convinced that he will not live up to the example set by Optimus Prime.
In the cartoons (though not necessarily later forms of G1 fiction), while Hot Rod has more of a magenta hue, Rodimus Prime is more of a maroon, and is a heavier, bulkier more "mature" version of Hot Rod. If Hot Rod were a teenager who just graduated high school, Rodimus Prime would be his post-college equivalent; Ready to enter the world, but unsure of his abilities.
After returning the Matrix to Optimus at the end of The Rebirth, Hot Rod retained much of the maturity he had gained as Rodimus Prime. He was content to settle into a role alongside Ultra Magnus as one of Optimus' highest-ranking Autobots, without assuming the role of leader.
Rodimus transforms into a maroon-and-orange Cybertronian Winnebago-style vehicle with yellow flame designs. Rodimus' vehicle mode resembles his Sports car mode as Hot Rod, with the addition of a trailer; similar to how Optimus Prime gains a trailer when he transforms into his truck mode.