This occurs at the molecular level. As electrons move through the material, some collide with atoms, other electrons, or impurities. It is these collisions that cause resistance. Heat causes molecules of the material to vibrate. These vibrations effectively increase the areas of possible collisions, thereby increasing resistance to current flow.
Most conductors increase in resistivity as temperature increases.
Carbon however, decreases in resistivity as temperature increases. This is also generally true for semiconductors, such as germanium and silicon. The resistivity of constantan is not affected by changes in temperature. For this reason, constantan is often used for precision wire-wound resistors with very low tolerances. For most conductors, resistivity decreases as temperature decreases.