Derek

Derek (otherwise just known as Paxman) is a diesel who was brought to help Bill, Ben, and Boco at the china clay quarry when the work load was getting too high. Derek had "teething troubles", however, and was prone to overheating and exhaustion. He tried to bank Bill and Ben up a steep slope, but he ran hot again, and he had to be carried up the hill with their train. The Fat Controller sent Derek to the works to make him better. Bill and Ben decided that he was actually very nice, despite his teething troubles. ("Double Teething Troubles")

Derek appears to have stayed on the railway, albeit largely out of view. He has been spotted pulling a train up Gordon's Hill. (Calling All Engines!)

Behind the Scenes
According to David Maidment, Season 5's railway consultant, Derek's exploits are based on failed attempts to have D95xx Paxman diesels bank CI 37s and their trains to Ebbw Vale. The bankers would run hot halfway up, leaving the engine to carry its load and the banker up the slope.