What is the etymology of the word "Flagrant"?

The Merriam-Webster online dictionary has two meanings for "flagrant:"

1. conspicuously offensive
2. fiery hot (archaic)

https://www.merriam-webster.com/dictionary/flagrant

The word has been in common use since about the sixteenth century. Somewhat unsurprisingly, the two meanings identified above are not far apart, etymologically speaking.

The Latin "flagrantem" meant "burning or glowing" with the more figurative sense of "glowing with passion, eagar". Going further back, the Proto-Indo-European (PIE) root leads to "bhleg" "to shine, flash or burn" from "bhel". The more common meaning today of "glaringly offensive, scandalous" was first seen in 1706, perhaps from the legal phrase "flagrante delicto" "while the crime is being committed, or red-handed." The literal sense of "in flagrante delicto" meant "with the crime still blazing."

https://www.etymonline.com/search?q=flagrant