YES.
You could call it an equilibrium.
It is when all bodies are at the same temperature.
No. When two bodies or regions are at the same temperature, equilibrium is already reached & no transfer of heat occurs.
If a hot body contacts a cold body, heat is lost to the cold body until both bodies reach the same temperature (reach equilibrium) after which, the two bodies cool down at the same rate.If two bodies of the same temperature come in contact, they would cool down together, as there is no difference in their initial temperature and their temperature is already in equilibrium.
temperature
Heat will flow from the body with the highest temperature to the lowest temperature body until the temperatures are the same.
Conduction is a mode of transfer of energy within and between bodies of matter, due to a temperature gradient.
Thermal Energy always transfer from the higher temperature to lower temperature until both bodies reach the same temperature or in thermal equilibrium with each other.
in case of transfer of heat. the heat is transferred from a body at higher temperature to the body at lower temperature. the heat is transferred till the time the temperature of both the bodies becomes same.
Systems (including heat systems) all tend to an equilibrium. What happens is the energy of the moving particles is transfered through contact (direct or indirect, such as by air) from the warmer, faster moving particles to the slower cold ones. After a time, the average kinetic energy of the two bodies is equal, and will trade energy at an equal rate (equilibrium).
By the principle of thermodynamics, the heat travels from one body which in contact with the other, till the point where both the bodies acquire same temperature, so conduction works in sync with thermodynamics where both bodies acquire same temperature.
When the temperature of each body is the same.