Born in Philadelphia, Pennsylvania, Temin studied biology at Swarthmore College and at the California Institute of Technology, where he obtained his PhD in animal virology in 1959. He worked at the University of Wisconsin from 1960 onward, serving as professor of oncology there from 1969 until his death from lung cancer.

There are two classes of viruses, those with DNA and those with RNA genes. The former replicate by transforming their DNA into new DNA and transmit information from DNA through RNA into protein. The latter class of viruses replicate RNA into RNA and transmit information directly into protein without the need for DNA. That is, all such reactions fitted into the general sequence DNA to RNA to protein, the so-called Central Dogma of molecular biology. In the early 1960s Temin discovered a curious feature of the RNA Rous chicken sarcoma virus (RSV): he found that it would not grow in the presence of the antibiotic actinomycin D, a drug known to inhibit DNA synthesis. Temin realized that this might mean the RSV replicated through a DNA intermediate, which he called the provirus. That is, Temin was proposing the sequence RNA (of the RSV) to DNA (provirus) to RNA (replicated RSV) which, while not actually excluded by the Central Dogma, was not implied by it either.

If such a reaction did take place then it would certainly require the presence of an enzyme capable of transcribing RNA into DNA. It was not until 1970 that Temin identified the enzyme (discovered independently by David Baltimore) known variously as reverse transcriptase or RNA-directed DNA polymerase. It was for this work that Temin shared the 1975 Nobel Prize for physiology or medicine with Baltimore and Renato Dulbecco.