Heenan came to the Cape of Good Hope in 1874, where he joined the Public Works Department as draughtsman and engineering assistant. Following the great floods of 1874 he was employed on bridge construction over the Fish and Koonap Rivers. Soon after his arrival he also reported on the feasibility of constructing hardened roads over the sands to Simon's Town. His specifications and plans were later used to build these roads successfully.

In 1876 Heenan was transferred to the East London and Queenstown Railway, then under construction, as assistant engineer, rising to district engineer by 1879. During the Frontier War of 1877-1878 he served as adjutant of the Kei Road district, with control over all its outposts, and was awarded a medal and clasp. In 1881 he became maintenance engineer of the East London to Queenstown Railway and the East London Harbour. Early in 1885 he was transferred to the Midlands system of railways as district engineer and settled in Port Elizabeth where he served the Port Elizabeth Harbour Board. By this time he was a member of the (British) Institution of Civil Engineers. He drew up plans for a new railway station at Port Elizabeth in 1890. From May 1894 he was resident engineer of the Port Elizabeth Harbour Board and developed the port so successfully that during the Anglo-boer War (1899-1902) the British Navy complimented him on having provided one of the finest naval bases in an open roadstead in the world. Among the important improvements that he instituted were the erection of hydraulic and electric cranes, the enlargement and strengthening of the jetties to enable sea-going vessels to berth alongside, and the expansion of the harbour. During these years he visited England several times.

He was presumably the same person as "H. Heenan", civil engineer, who was listed as a member of the South African Philosophical Society in 1883. Whatever the case may be, R.H.H. Heenan joined (or re-joined) the society in 1891, when his affiliation was given as the Table Bay Harbour Works. He remained a member until some time between 1900 and 1906. In 1897 he wrote a paper on "The harbour of Algoa Bay, Cape Colony", that was published in London by the Institution of Civil Engineers.

In 1900 Heenan was appointed engineer to the Table Bay Harbour Board and settled in Cape Town. That same year he became a member of the Cape of Good Hope Meteorological Commission, serving to 1906. He travelled to England, continental Europe and the United States to visit various harbours and to order the latest machinery for Cape Town. After his return in 1901 he was appointed general manager and engineer-in-chief of the Table Bay Harbour Board, and developed the harbour into one of the finest in Africa. During 1905 he drew up several plans of the harbour, indicating a proposed pier, reclamation of land, railways, etc. He retired at the end of 1908 when the Harbour Board was abolished and settled in England. In 1922 he emigrated to the United States of America.

Heenan was a founding member of the Cape Society of Civil Engineers, which held its first meeting in January 1903, serving as joint vice-president from 1903 to 1905 and as president in 1906. However, he was no longer listed as a member in 1907. In October 1904 he read a paper, "Notes on harbours", before the society. By 1913 he was an honorary member (the only one) of the society's successor, the South African Society of Civil Engineers, and resided in London. By 1903 he was a member of the South African Association for the Advancement of Science (founded in 1902) and two years later joined the British Association for the Advancement of Science when it met in South Africa. By that time he had become a member also of the (British) Institution of Electrical Engineers. His diaries are kept in the Cape Town Archives Repository.

Heenan was married to Edith Maria Fuller in 1878 and they had five children.