The award is named in honour of British scientist Sir Benjamin Thompson, Count Rumford, who is noted for his works on thermodynamics and for establishing the Royal Institution.

The award was created in 1796 after Thompson transferred £1,000 to the Royal Society in stocks, instructing the latter to grant the awardee the fund's interest as a premium.

The obverse featured a tripod altar with a flame upon it, circumscribed by a Latin inscription from Lucretius' poem De rerum natura "Noscere quae vis et causa".

The reverse has the Latin inscription "Optime In Lvcis Caloqisqve Natvra Exqvirena Merenti Adivdicat Soc: Reg: Lond."

("The Royal Society of London awards this to one outstandingly deserving in investigating the nature of light and heat") inscribed within a wreath of oak and laurel leaves bound with ribbons.

[1] Ten times during the early 19th century, no medals were awarded due to the unavailability of suitable candidates or political considerations of the Royal Society Council.