Final answer:
A black hole with the mass of the Moon would be extremely cold, since black holes do not emit heat. However, the matter in the accretion disk around the black hole could heat up significantly, emitting X-rays and reaching temperatures of millions of degrees, creating an environment that is extremely hot.
Step-by-step explanation:
If a black hole had the mass of the Moon, it wouldn't be very hot in terms of temperature since black holes themselves do not emit radiation that we can associate with heat. However, if we consider the environment around the black hole, particularly the accretion disk where matter gets extremely heated up due to friction and gravitational forces, then we would see different behavior. The correct answer in the typical sense would be a) Extremely cold, as the black hole itself doesn't possess heat in the way we understand it. However, if gas accumulates around such a black hole and forms an accretion disk, it's the infalling matter in this region that would heat up quite significantly. Gas approaching the event horizon can heat up to temperatures of millions of degrees, sending out X-rays and other forms of radiation before it crosses the event horizon. Therefore, the region close to the event horizon would be deemed extremely hot due to the heated matter, not the black hole itself. In contrast, the black hole's surface, or the event horizon, does not have a temperature we can measure like traditional objects as it does not emit radiation.
When considering what a black hole 'has to work with' in terms of temperature, we refer to the streams of infalling gas which heat up dramatically as they increase in speed due to the black hole's immense gravity. For example, gas near a supermassive black hole can reach 150,000 K, and even more under certain conditions. This is an illustration of how the gas's kinetic energy converts into heat energy, similar to a spacecraft reentering Earth's atmosphere. However, the temperatures achieved near a black hole are far greater due to the extremely high speeds of infalling matter.
It's worth noting that the environment a black hole creates in terms of temperature is vastly different from the black hole itself. Absorptive surfaces like a black hole's event horizon are a perfect blackbody, meaning they do not reflect radiation and are considered perfectly absorptive.