His father James was professor of mathematics at the University of Glasgow from 1832 onward and his younger brother William was to become Baron Kelvin.

He remained there until 1873, when he accepted the Regius professorship of Civil Engineering and Mechanics at the University of Glasgow (in which post he was successor to the influential William Rankine) until he resigned with failing eyesight in 1889.

His proposers were his younger brother William Thomson, Peter Guthrie Tait, Alexander Crum Brown, and John Hutton Balfour.

Also 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 glacier motion, where he extended the work of James David Forbes.

He studied the experimental work of his colleague Thomas Andrews, concerning the continuity of the liquid and gaseous states of matter, and strengthened understanding of it by applying his strong knowledge of thermodynamics.