Conductivity matters. Copper pans that are thick heat-up really fast. This is one of their primary benefits in that they change temperature quickly based on the input. The heat-up and cool down quickly. This is why they are popular with chefs - fine tuned control on pan heat which you generally want to change while cooking.

Cast iron is the opposite. They take a long time to heat-up and a long time to cool down. Steel is somewhere in between.