Arthur Heatlie was a son of Thomas T. Heatlie, member of the Cape Legislative Council, and a brother of the surveyor Bertram de Vos Heatlie*. He was educated at Peterhouse, University of Cambridge, where he was awarded the degree Bachelor of Arts (BA). An accomplished sportsman during his student days, he rowed in his College's first team of eight for three years, and in 1885 won an underwater swimming championship in Cambridge with an amateur record distance of 83 meters. In September 1894 he married Lucy Mann, daughter of William Mann* of the Cape Royal Observatory, and granddaughter of Thomas Maclear*.
Heatlie entered the civil service of the Cape of Good Hope as an engineering assistant in the Public Works Department in October 1885 and worked in the Eastern Cape from 1886 to 1888. He was promoted to assistant railway engineer on the Junction and Indwe railway surveys in November 1888 and then worked in the Free State on railway construction and various surveys to June 1896, when he became assistant maintenance engineer at Port Elizabeth. After two years at East London from March 1897 he was promoted to district engineer, Cape Government Railways, in January 1899, serving at De Aar, Queenstown (from January 1903), and Salt River (from May 1905).
Heatlie was at first an associate member of the (British) Institution of Civil Engineers, becoming a full member about 1903. During that year he also joined the Cape Society of Civil Engineers (founded late in 1902). In March and November 1905 he read two papers before this society, one on "Kloppersfontein water supply, Sterkstroom-Eastern System", the other on the "Lesseyton Bridge wash away". He was still a member of the society's successor, the South African Society of Civil Engineers, in 1913 and during 1912 read "Some notes on the Wolseley to Ceres Railway construction" before its members (Minutes of Proceedings, 1912, Vol. 10, pp. 77-84). By 1910 had been promoted to engineer-in-charge, Ceres Road to Ceres Railway, and was living in Ceres. He appears to have remained there to at least 1930.
Heatlie was a foundation member of the South African Association for the Advancement of Science in 1902, and served as a member of the local committee for Queenstown in 1907/8.