Locally we can see things tend to go to equilibrium.
A basic overview.
Put a pot of hot water on the counter and mass of the room and the pot of water come to an equilibrium temperature. Assuming mass of room and all its contents are much greater than the pot of water and the room is well insulated practically speaking you can say the pot of water cones to room temp. To the pot as a source the room and its mass is the ultimate heat sink.
But heat goes through the walls to the outside environment. To us on the Earth the ultimate sink is the CMBR which looks like a black body at about 3 degrees K.
So the Earth wants to go to equilibrium with the CMBR.
Put a spherical black body deep in space at 100c. It simultaneously absorbs energy from the background and radiates energy away. As long as the sphere temp is greater than the background temp more energy will be radiated than absorbed..When the absorbed radiation equals the radiated energy the sphere is in equilibrium with the background.
Ignoring mass like atmosphere that escapes into space the Earth is a black body. Energy leaves and arrives by radiation.
Some incoming radiation is reelected some absorbed. Some of the heat generated in the environment is radiated away. Heat that does not escape shows up as a rise in temperature.
In a one room cabin out in the open in the winter turn on an electric heater. If the amount of heat generated by the heater is greater than the heat leaving through the walls room temp goes up.
If the Space Shuttle could not open the cargo bay doors exposing the radiators it would overheat and have to come down.
Internal natural heat in the Earth comes from things like natural fission, hot core, and plate tectonics. Plus human created heat. Plus net solar radiation absorption.
When heat on the Earth is greater than the radiated heat temp goes up. How heat is distributed in the environment is climate sconce.
Amount of heat radiated per second into s[ace depends on emissivity and total surface area.
Earth's surface emissivity is a unitless value that measures its efficiency in emitting thermal infrared radiation, with a global average surface emissivity of about 0.95. However, the emissivity varies by location, with deserts having lower values (around \(0.65\)-\(0.99\)) and areas with vegetation, water, and ice having much higher values (above \(0.95\)). This variation is due to differences in surface composition.
Plenty of info on the net on thermal radiation, radiative cooling, and black bodies.
I do not think the Earth has ever been in any kind of equilibrium state. Surface conditions have been in a variable zone that allows life as we know it.
Ice ages come and go.