I'm reading my first book on physics "Seven brief lessons on physics" by Carlo Rovelli, and in his chapter on "Probability, time and heat of black holes", he mentions that Stephen Hawking showed that black holes are hot, they emit heat. My question is, does the earth emit heat?
Yes; but not for the same reason as a black hole.
Every object emits electromagnetic radiation with an energy corresponding to it's surface temperature.
Earth emits heat; but it also absorbs heat from radiation. In the light of the sun for example, more radiation is absorbed by the planet than emitted, so it heats up; but the Earth is still emitting that thermal radiation.
Yes, Earth emits heat; radioactive minerals in the crust and core are continually decaying (potassium-40 and uranium in particular)and the decay releases energy which percolates upward through the ground as heat. Volcanoes and hot springs are the more spectacular evidences of this, but there is lesser geothermal heatflow, from below, everywhere.
Earth also exchanges heat with (for instance) sunlight and the cold dark sky. The heat income from sunlight and geothermal heat balance the loss of heat to the dark sky, at the surface temperature we call 'temperate'.
The net emission (not including secondhand heat from the Sun) of heat is the geothermal contribution, plus some human-generated minor additions.