Robert Templeton was the son of John Templeton and was educated in Belfast Academical Institution, which was in part his father's creation. In 1821 he left Ireland for Edinburgh, Scotland to study medicine and following graduation practised in the University hospital. In 1833 (6 May) he was commissioned as Assistant Surgeon in the Royal Artillery, initially stationed at the Royal Artillery Barracks, Woolwich, close to London, England.
In 1834 Templeton was stationed to Mauritius and in 1835 to Rio de Janeiro and Recife. From Rio (1835) he took ship to Colombo, Ceylon, via the Cape of Good Hope and in this year became a Corresponding Member of the Zoological Society of London. A brief sojourn in Ceylon was followed by a stay in Malta (1836). Later in 1836 he moved on to Corfu and Albania. In all these places Templeton collected insects and other invertebrates and in 1839 he became a Corresponding Member of the Entomological Society of London.
A twelve year stay in Ceylon (1839–1851) followed, and in 1847 Templeton was promoted from Assistant Surgeon to Surgeon. Recalled from Ceylon in 1852 due to the unrest in Europe which was to erupt in the bloody and terrible Crimean War, he served in the Crimea from March 1854–1856 and was promoted to Surgeon-Major on 7 December 1855. He retired with the honorary rank of Deputy Inspector General of Hospitals on 31 January, 1860.
Templeton was particularly interested in the Thysanura and his first published entomological paper concerns these insects. Thysanurae hibernicae (Irish bristle tails and spring-tails) was published in the first volume of the Transactions of the Entomological Society of London for 1836 and is the first significant work in English on these primitive insects, remaining so until 1875. In this short work prefaced by John Obadiah Westwood Templeton described two new genera and twelve new species accompanied by two plates showing whole animals and details of structure. Forty years later the entomologist Lubbock paid tribute to Templeton's early work by naming a thysanuran genus after him — Templetonia.
Much of Templeton's early work and very much in Ceylon was on spiders. Studies of Irish spiders were passed to John Blackwall who incorporated the notes and drawings into his own work. Oddly, although he collected my old pets the spiders, he published nothing on them.
In Ceylon Templeton worked mainly on Lepidoptera, Coleoptera and Hymenoptera alongside Edgar Leopold Layard (1824–1900). New species of Lepidoptera collected by Templeton and Layard were described by Frederic Moore, Francis Walker and George Robert Gray. The new Coleoptera were described by Joseph Sugar Baly, Francis Walker, John Obadiah Westwood, Carl August Dohrn and Francis Polkinghorne Pascoe. Templeton's publications on Lepidoptera amount to some general comments on papilionid butterflies and two species descriptions — Oiketicus terlius and Oiketicus (Cryptothelia) consortus. The bulk of the new beetles, some of the Hymenoptera (the rest were described by Frederick Smith) and other insects in Templeton's collection were described by Francis Walker who also compiled the first list of the insects of Ceylon for Tennent's book Ceylon based on the collections of Templeton, Layard, the British Museum and the Museum of the East India Company; there are 2,000 species and Layard and Templeton captured between them 932 species of butterflies and moths in Ceylon many, new to science. Templeton supplied many of the insects incorporated in Westwood's book Oriental Cabinet, one of which, the beetle Compsosternus templetonii bears his name. Unfortunately only the published part of Templeton's correspondence with Westwood (the Secretary of the Entomological Society) survived, the manuscripts are apparently lost. Templeton's Ceylon insect collection was apparently divided between the Belfast Museum (now in the National Museum of Ireland), the Entomological Society of London and the British Museum (the Entomological Society's collections are now incorporated in those of the latter institution). Templeton's watercolour paintings of Ceylon butterflies are in the Ulster Museum, Belfast. Templeton, Layard and Thwaites and later John Nietner (died 1874) contributed almost all that was known of the insect fauna of the island at the end of the first half of the nineteenth century including a privately printed list of Thysanura, Myriapoda, Scorpionidae, Cheliferidae and Phrynidae (now Amblypygi) from Ceylon which is not traced, and remarked on the habits of the large poisonous centipedes Scolopendra pallipes and S. crassa in two (published) communications to Westwood.
Part of Templeton's Mollusca collection was described as comprising several new and rare species hitherto undescribed. Amongst others are new species of each of these genera: Achatina, Helix, Neritina, Ampullaria, Valvata, Planorbis and Melania. Robert Templeton sent back to the Belfast Museum specimens of the Ceylonese pearl mussel showing growth stages of the mussels from the famous pearl fisheries of Ceylon. He also described two species of land-slug (Vaginula maculata and Parfnacella tennenti) from Ceylon. It was Templeton who described the extraordinary Giant Earthworm Megascole caeruleus from Ceylon which is between 20 and 40 inches long and has a thickness of nearly an inch or more.
Templeton also studied the vertebrates of the island, especially the fish, birds and monkeys. Amongst the birds were five endemic species new to science. These were described by Edward Blyth in the Calcutta Journal as Athene castanotus, the chestnut-winged hawk owl; Malacocercus rufescens, the red dung thrush; Dicrurus edoliformis, the kingcrow, Dicrurus leucopyygialis the Ceylon kingcrow, and Eulabes ptilogenes , Templeton's mynah. The monkeys were studiously appraised and some of the results communicated to the Zoological Society of London. These communications, one of the monkey Cercopithecus pileatus and the loris Loris gracilis and the other on a supposed new species Semnopithecus leucoprymnus cephalopterus which turned out to be identical with Bennet's Semnopithecus nestor, are Templetons only personal contribution to the literature on the vertebrates of Ceylon. His knowledge of the smaller mammals, birds, reptiles and fishes was instead incorporated in the work of others, notably George Robert Waterhouse and his coworker Edgar Layard who in the introduction to Notes on the ornithology of Ceylon says I have had the advantage of consulting with Mr. Blyth and Drs. Templeton and Kelaart with each of whom i have been on terms of the closest intimacy and we mutually communicated our discoveries