Tembo was born on September 14, 1932 in Dedza District, Central Region. His father, Zenus Ungapake Tembo, was a minister of the Church of Central African Presbyterian (CCAP). He attended several primary schools before graduating to Blantyre Secondary School. He later went to study at the University of Roma (also known as Pius XII College) in Lesotho, graduating in 1958 with a Bachelor of Arts in political philosophy. He had a brief stint as a teacher at Dedza Secondary School and later taught for two years at Robert Blake Secondary School in the central region district of Dowa in 1958.