How does the resistance of a conductor change with a rise in temperature?

In a conductor the number of electrons in unit volume of the conductor is almost independent of temperature. However, the relaxation time does vary with temperature. When temperature increases, the thermal speed of the electrons increases as well as, the amplitude of vibration of the positive ions inside the metal conductor also increase, about their mean positions. Thus, the collisions between the electrons and the positive metal ions become more frequent and this decreases the relaxation time, t, leading to an increase in the resistivity of the conductor.
Also, the temperature coefficient of metals is positive.