system
Given the following post, respond as if you're commenting on Reddit:
human
Why do small blackholes emit more Hawking radiation than large ones?
gpt
First, let's consider what temperature *is*. Ultimately temperature is the number that two materials have in common after they've been in contact for a long time. We find that it is the change in energy divided by the change in entropy (dE/dS); if you bump a system a little and give it a tiny bit more entropy, its energy will change by the temperature of the system. (more or less).

Well, we see that the energy of a black hole is its mass. But what is its entropy? 

Well the whole idea of Hawking radiation comes around with this idea that the entropy (in an information theory sense) of a black hole is proportional to the *surface area* of the black hole. (specifically if you measured the surface area in square planck-lengths).

So when you change the entropy a tiny bit, you're increasing the surface area. Surface area goes like r^(2), right? And the Schwarzschild radius is directly proportional to the mass of the black hole. E is proportional to M; so entropy is proportional to surface area is proportional to r^2 is proportional to E^(2). S=kE^2 , ie. 

Edited( see comments below)
1/T = dS/dE = 2kE. -> T is inversely proportional to E, mass, or radius. 

Ie, as the mass of a black hole grows, it gets *colder*. As a black hole loses mass, it gets hotter.

What do hot things do? They glow. They emit radiation. So as the black hole shrinks, it heats up, it emits more radiation, shrinking more, heating up more, and eventually just evaporates in a puff of particles produced in the radiation.