Does the internal energy of the conductor through which the electric current flows change?

The conductor has a crystal lattice, and the current is the directional movement of electrons. When electrons move on their way, they collide with the nodes of the crystal lattice in which the atoms are located. Electrons collide with lattice sites. As a result, the conductor heats up through which the electric current flows, its internal energy increases.
According to the Joule-Lenz law, in a conductor through which an electric current flows, an amount of heat is released Q = I * U * t. Where I is the current strength, U is the voltage at the ends of the conductor, t is the time of passage of the electric current.