An electric current that passes through a metallic wire produces heat because of :

A metallic conductor has a large number of free electrons in it. When a potential difference is applied across the ends of a metallic wire, the free electrons begin to drift from the low potential to the high potential region. These electrons collide with the positive ions (the atoms which have lost their electrons). In these collisions, energy of the electrons is transferred to the positive ions and they begin to vibrate more violently. As a result, heat is produced. Greater the number of electrons flowing per second, greater will be the rate of collisions and hence more heat is produced.
Hence, The electric current passing through a metallic wire produces heating because of collisions of the conduction electrons with the atoms of the metallic wire.