While William Thomson, Lord Kelvin, is renowned for his work as a physicist and engineer, he was also active in politics. He was a staunch Liberal, and considered standing for the constituency of Aberdeen and Glasgow Universities in 1869. Thomson declined however, as he was advised that the work required for him to be elected would keep him from his teaching and research work.
Thomson remained a Liberal, until the Second Home Rule Bill was introduced, after which he was a devoted Liberal Unionist. Indeed, he was a notable leader among the Liberal Unionists in the west of Scotland, and it has been suggested his ennobling was just as much for his political activity as for his scientific work.
Let's say Kelvin is elected to Parliament in 1869, where can he go from here? He's a respected public figure, so it's possible Gladstone could give him a minor cabinet post. Kelvin could gradually work up from there, until he's invited to become PM in the 1880s or 90s. Could Kelvin have a shot at being a decent, or even good PM, and how will his scientific work suffer as a result?