After completing secondary school in Vienna-Ottakring, Othmar Kühn worked in the brewery in Hallein, returned to Vienna in 1914 and enrolled to study natural sciences, specializing in botany, at the University of Vienna. He qualified as a secondary school teacher in 1916 before being enlisted into the army. He was severely wounded at the Second Battle of the Piave River in 1918. The following year he obtained his doctorate in botany, with palaeontology as a subsidiary subject, at the University of Vienna. He worked afterwards as a secondary school teacher in Vienna and as an intern in the geopalaeontological department of the Naturhistorisches Museum (NHM). According to his application for readmission into the NSDAP in May 1938 and an undated CV, he was already a National Socialist in 1919 and co‑founder of the NSDAP in Austria, author of several flyers and brochures, keynote speaker at two Party conferences and speaker at rallies in Czechoslovakia. In 1925 he left the Party as a result of internal disputes and joined the gewerkschaftliche Vereinigung der Mittelschullehrer (Trade Union Association of Secondary School Teachers), later described in Nazi sources as a "red combat unit", remaining in it until it was disbanded in 1934 under the Austrofascist regime. The political assessments of Kühn during the Nazi era were therefore sceptical or negative. In April 1940 he was readmitted to the NSDAP after he had joined the Nationalsozialistische Volkswohlfahrt (National Socialist People's Welfare) and Nationalsozialistischer Lehrerbund (National Socialist Teachers League). In May 1940 he was conscripted into the Wehrmacht, serving as a military geologist on the Eastern front and in France, before he was discharged in 1943 as being unfit for service on account of his First World War wound. The Reichsministerium für Wissenschaft, Erziehung und Volksbildung (Reich Ministry of Science, Education and Culture) proposed him as head of the geology and mineralogy section of the Institut für Deutsche Ostarbeit (Institute for German Work in the East – a research institute) on the premises of the closed University of Kraków. Instead, however, he took over the position of Julius Pia (1887–1943) as head of the geopalaeontological department at the NHM, where he was promoted to Kustos I. Klasse (curator 1st class) on 1 May 1944.
In July 1945 he had himself registered as a National Socialist and was classed as a lesser offender. His application to be removed from the register of National Socialists and to be part of the reconstituted staff of the NHM was granted in 1948, and in 1949 he was appointed department head. He became an ordinary professor of palaeontology at the University of Vienna in 1951, was appointed dean of the Philosophy Faculty in 1956/57 and then rector and chairman of the österreichische Rektorenkonferenz (Austrian Conference of University Rectors) in 1960/61. After his retirement in 1964 he returned to his former position at the NHM and published diverse academic works. He was to receive the Goldene Ehrenmedaille der Stadt Wien (Golden Medal of Honour of the City of Vienna) on 11 March 1969 but was unable to accept it in person for health reasons. He died two weeks later. He became an object of systematic provenance research because while a military geologist in the Second World War he had brought thin sections of algae from occupied Ukraine to the NHM. The lack of documentation made it impossible, however, to determine further details of their acquisition.