He at first intended to take holy orders, but afterwards he applied himself to the study of medicine, and went in 1736 to the university of Leyden, where he attended the lectures of Dr. Herman Boerhaave, and was created M.D.

In 1750 he was introduced to Dr. John Fothergill with a view to institute a medical society in order to procure the earliest intelligence of improvements in physic from every part of Europe, but the plan never took effect.

When the British Museum was opened in 1758, for purposes of inspection and study, Templeman was appointed on 22 December to the office of keeper of the reading-room.

Templeman resigned the post on 18 December 1760 on being chosen secretary to the recently instituted Society of Arts, Manufactures, and Commerce.

Bowyer says ‘he was esteemed a person of great learning, particularly with respect to languages, spoke French with great fluency, and left the character of a humane, generous, and polite member of society.’ A portrait by Richard Cosway belongs to the Society of Arts, and was engraved by William Evans.