hawking radiation is a postulated mechanism for tempurature of a black hole.

the whole thing started with information paradox, leading to the suggestion that a black hole would have to be associated with entropy, thus would have a temperature, but required an escape hatch to allow radiation, the thought experiment came to a thought solution when particle-antiparticle pair dissociation at the event horizon was postulated.

We Knew Black Holes Have a Temperature. It Turns out They Also Have a Pressure[2021]:

https://www.universetoday.com/articles/we-knew-black-holes-h...

Black hole thermodynamics:

https://en.wikipedia.org/wiki/Black_hole_thermodynamics