Roger Temam completed his undergraduate and graduate studies in mathematics at the University of Paris earning his Licence in 1960, Agrégation de Mathématiques in 1962 and Doctorat-és-Sciences in 1967. Upon completing his undergraduate studies he was appointed assistant professor of the Faculté des Sciences de Paris and was promoted to associate professor in 1968 at the Faculté des Sciences d'Orsay. From 1972 to 1980 he was Professor at the Université Paris-Sud, was given the distinguished title Classe Exceptionelle in 1981 and Emeritus Professor in 2003. Since 1986, he has been Director of the Institute for Scientific Computing & Applied Mathematics at Indiana University Bloomington and since 1994 he has been College Professor of Mathematics. He has held visiting appointments at the University of Colorado and Brown University.

Described as "among the five best and most influential applied mathematicians alive today," Professor Temam is credited with defining the domain of discourse in several large areas of applied mathematics, including numerical computation of fluid flows, slow dynamics and intertial manifolds, turbulence theory, and climate modeling. He is regarded as one of the top experts in mathematical models for climatology and a leading expert worldwide in nonlinear partial differential equations and their applications. Professor Temam's synergetic work played a crucial role in the early development of mathematical geophysical fluid dynamics and in engaging collaborations between mathematics and geosciences. The scientific work of Professor Temam is vast and has had lasting impacts in mathematics and applications to the sciences, engineering and human development.

Temam's publication record is ranked 24th overall in field strength by Microsoft Academic Search, among all mathematicians in all fields, and according to the Harzing's counting Temam has been cited over 25,000 times. Temam has given numerous distinguished lectures, notably speaking at the International Congress of Mathematicians (a lifetime distinction). He is considered the "most prolific advisor in mathematics" according to the Mathematics Genealogy Project with 112 Ph.D. students and 407 mathematical descendants, including distinguished mathematicians around the world. In sum, "It would be difficult to overestimate the impact of Roger's presence over the years on the reputation of the Mathematics Department of Indiana University."

Temam has received the College de France Prix Peccot Award, Seymour Cray Prize in Numerical Simulation, and in 2012 was knighted with a Légion d'Honneur in France. He has been named Honorary Professor by Fudan University, Xi'an Jiaotong University, and Lanzhou University in China and has been elected Fellow of the Society for Industrial and Applied Mathematics, the American Association for the Advancement of Science, and the American Mathematical Society. The French Academy of Sciences has recognized Temam's work four times; with the Prix Carriére in 1977, the Grand Prix Alexandre Joannidés in 1993 and 2003, and by naming him a Fellow of the French Academy in 2007.

Temam received the IU Bicentennial Medal in September 2020 in recognition of his distinguished contributions to Indiana University.