One end of a rod is held in a fire, while the other is held by one’s hand. Just assume his hand doesn’t get burned. After some time the rod-hand system is in thermal equilibrium. True or False?

Heat is the flow of energy from a high temperature to a low temperature. When these temperatures balance out, heat stops flowing, then the system (or set of systems) is said to be in thermal equilibrium. Thermal equilibrium also implies that there's no matter flowing into or out of the system.