Thomson spends much of his youth in Glasgow. His father James is professor of mathematics at the University of Glasgow from 1832 onward. He attends Glasgow University from a young age and graduates in 1839 with high honors in his late teens. After graduation, he serves brief apprenticeships with practical engineers in several domains. He then gives a considerable amount of his time to theoretical and mathematical engineering studies, often in collaboration with his brother, during his twenties in Glasgow. In his late twenties he enters into private practice as a professional engineer with special expertise in water transport. In 1855, he is appointed professor of civil engineering at Queen’s University Belfast. He remains there until 1873, when he accepts the Regius professorship of Civil Engineering and Mechanics at the University of Glasgow in which he is successor to the influential William Rankine. He serves in this position until he resigns with failing eyesight in 1889.
In 1875 Thomson is elected a Fellow of the Royal Society of Edinburgh. His proposers are his younger brother William, Peter Guthrie Tait, Alexander Crum Brown and John Hutton Balfour. He is elected a Fellow of the Royal Society of London in June 1877. He serves as President of the Institution of Engineers and Shipbuilders in Scotland from 1884 to 1886.
Thomson dies of cholera in Glasgow on May 8, 1892. He is buried on the northern slopes of the Glasgow Necropolis overlooking Glasgow Cathedral. One obituary describes Thomson as “a man of singular purity of mind and simplicity of character,” whose “gentle kindness and unfailing courtesy will be long remembered.”
Thomson is known for his work on the improvement of water wheels, water pumps and turbines. He is also known for his innovations in the analysis of regelation, i.e., the effect of pressure on the freezing point of water, and his studies in glaciology including glacial motion, where he extends the work of James David Forbes. He studies the experimental work of his colleague Thomas Andrews concerning the continuity of the liquid and gaseous states of matter, and strengthens understanding of it by applying his strong knowledge of thermodynamics. He derives a simplified form of the Clapeyron equation for the solid-liquid phase boundary. He proposes the term triple point to describe the conditions for which solid, liquid and vapour states are all in equilibrium.
Thomson also makes contributions in the realm of fluid dynamics of rivers. It is claimed that the term torque is introduced into English scientific literature by Thomson in 1884.