Why does a metal spoon dipped in a glass of hot tea not immediately heat up?

A spoon dipped in tea does not immediately heat up, because in nature all actions are limited by the speed of interaction. For example, in a spoon dipped in tea, the heating rate is limited by the rate of vibration of atoms in the metal lattice. Each physical body is characterized by a value, coefficient of thermal conductivity λ, which has a dimension of W / (m * K). Each substance has its own coefficient of thermal conductivity. And the thermal conductivity itself also depends on the temperature difference between the media.