In 1954 he joined Imperial College as a Reader in Applied Heat, in 1958 he was appointed Professor of Heat Transfer and was subsequently also Head of the Computational Fluid Dynamics Unit. He held both positions until his retirement in 1988.

At various times, he has been visiting Professor at MIT, the University of California, Berkeley, and the University of Minnesota; in the late 1970's he was Reilly Professor of Combustion at Purdue University

Professor Spalding has written many scientific publications from as early as 1949 with papers on thermodynamics, followed by publications on combustion, heat transfer, boundary-layer theory and computational fluid dynamics.

Professor Spalding's main honours and awards include:-

Fellowship of the Royal Society 1983
Fellowship of the Royal Academy of Engineering 1989
Max Jakob Award 1978
Bernard Lewis Medal 1982
Luikov Medal 1986
Foreign Membership of the Ukrainian Academy of Sciences 1996

In 1974, Professor Spalding founded the company, Concentration Heat and Momentum Limited, (known as CHAM) and remains its Managing Director. Its major product is the widely-used PHOENICS computer code, of which Professor Spalding is the main creator and continuing developer.