Usage of "burn" as a form of mockery - How did it start?

According to the UD burn (as a form of mockery) is an slang expression made popular by the "That 70's show," which ran from 1998 to 2006:

• (slang): to disrespect someone (to diss); to make fun of someone; used by a third party after a first party makes fun of a second party. Brought back to life by the ever-popular That 70's show.

According to Wiktionary, the noun burn has the following meaning (No. 5) that fits in your context:

(slang) An intense non-physical sting, as left by an effective insult.

The above meaning is derived from its No. 1 meaning:

A physical injury caused by heat, cold, electricity, radiation or caustic chemicals.

The OED (in a 2019 draft addition) references the 1942 American Thesaurus of Slang: "Disparaging or sarcastic remark; gibe" Its next earliest quotation is from the film Clueless in 1994:

Elton. You've been flirting with me all year. Cher. As if! I've been trying to help you and Tai get together. Elton. What a burn. Why would I go with Tai?"

It's also in Merriam-Webster ("used chiefly in the phrase sick burn") and other dictionaries, so no need to go to Urban Dictionary.

The origin seems to relate either to causing pain, causing redness of the cheeks (or backside), or some combination. I can't find any good evidence about this.

Reference: "burn, n.3." OED Online. Oxford University Press, June 2021. Web. 20 August 2021.