'slow-burn' is a compound formed from two Old English elements: 'slow' (from Old English 'slaw'), where 'slaw' meant 'not quick', and 'burn' (from Old English 'bærnan'/'beornan'), where 'bærnan' meant 'to be on fire or to burn'.

'slow' remained relatively stable from Old English through Middle English as terms meaning 'not quick', and 'burn' likewise existed as a verb meaning 'to be on fire'; the literal phrase indicating something that burns slowly developed later into a figurative compound in modern English to describe gradual intensification.

Initially it could be understood in a literal sense ('to burn slowly' or 'to keep burning with low flame'), but over time the compound has evolved into a primarily figurative meaning: 'a gradual build-up of intensity or feeling.'