James Watt was a scientist that the First Doctor heavily implied had a hand in developing steam power. He once used Watt as an example of how the most important discoveries could come from the tiniest details. When Ian wondered why the Doctor was so concerned about a mere lost button, the Doctor snapped that he had been with Watt when Watt noticed steam coming out of a kettle. This, the Doctor implied, led to one of Earth's "greatest discoveries". (TV: The Space Museum)
In the 19th century, he was expected in a scientific meeting in Killingworth sponsored by Lord Ravensworth and hosting George Stephenson, among the others. The meeting was supposedly cancelled after the plots of the First Rani and the Tremas Master, thwarted by the Sixth Doctor. (PROSE: The Mark of the Rani)
In 2009, the Tenth Doctor spoke to Malcolm Taylor about a wormhole that had formed between Earth and San Helios, the latter using a unit of measurement named after himself while describing it. When the Doctor enquired about it, he responded that it didn't do James Watt any harm. (TV: Planet of the Dead)