Thieme was born in Fort Wayne, Indiana to Anna (Cloakey) and Robert Bunger Thieme, and was raised in Beverly Hills, California. There he attended Beverly Hills High School which included four years of study in Latin. His undergraduate studies were at the University of Arizona at Tucson where he majored in Greek, and was elected to Phi Beta Kappa after graduating with honors in 1940. While attending university he met and married Betty Beal, the daughter of a Baptist minister.
Thieme's seminary studies at Dallas Theological Seminary were interrupted by World War II service, where he rose to the rank of lieutenant colonel in the Army Air Corps, and was in charge of training all Army Air Corps cadets at Luke Field. After World War II he resumed his theological studies at DTS where he graduated Magna Cum Laude. His 1949 Master's thesis was entitled Armageddon: An Investigation of the Campaign of the Great Day of God the Almighty. During his time at DTS, he held a part-time pastorate at Reinhardt Bible Church in Dallas, Texas.
Thieme became pastor of Berachah Church in Houston, Texas in 1950, interrupting his doctoral work at DTS after Dr. J. Ellwood Evans recommended him to the church. He was pastor at Berachah Church until he retired in 2003 due to Alzheimer's disease. Thieme dedicated his life to intensive study of the scripture and teaching his congregation. Gifted in intellect and indefatigable in production, Thieme held Bible classes most nights of the week and twice on Sundays. Requiring strict academic discipline from his congregation as well, he earned the genuine respect of those in regular attendance. Those close to him knew him as humble and gentlemanly. Over the years Thieme spoke at numerous Bible conferences, and ordained dozens of men to the ministry. His recorded Bible classes and books are available free of charge.
After retiring in 2003, Thieme's only son, Robert "Bobby" Thieme III, was elected by the congregation of Berachah Church to serve as the new pastor. Around this time R. B. Thieme, Jr., Bible Ministries began reformatting and revising existing material into modern formats (e.g. DVD and MP3).