For some time in the 19th century, it was believed that certain observed anomalies in the orbit of Mercury could be explained by the presence of a planet even closer to the sun, which was dubbed "Vulcan." Nobody ever found Vulcan, and eventually Einstein showed that these anomalies could be explained by general relativity instead.
Given the mythological names used for all the other planets in the Solar system, "Vulcan" is a pretty obvious name to use (especially for a hot planet). But it's still kind of funny that it's the name of both a very well-known fictional planet and a very well-known theorized-but-nonexistent planet.
Is there any evidence that Roddenberry was thinking of the hypothetical 19th-century planet when he named Spock's homeworld? Or did he get the name straight from Roman mythology?