The basis of this effect is kinetic molecular theory - which means that the particles in all matter are always in motion as long as the temperature is above absolute zero. Their rate of motion is directly related to the temperature of the material.
So in a copper wire the atoms are constantly interacting and vibrating. When a current is passed through the wire it, in a sense, has to force its way through the material in the wire. This results in internal friction which then produces heat. The heat, in turn, causes the particles to move even faster, producing more heat and more resistance.
So the higher the temperature of a material, the more resistance the material has.
This phenomenon also is at work in high voltage transmission lines. Much of the energy produced at the power plant is lost as the current flows through the lines to the end users.
Engineers have proposed cooling these lines to relatively low temperatures to decrease the resistance of the current in the lines. If the temperature is reduced enough, to the critical temperature of the material, the resistance disappears and the material becomes a superconductor. Much research is being done to find alloys whose critical temperature is relatively high so not as much energy is needed to cool them down.