Cold and Cool Vs Hot and Warm

Cold suggests a lower temperature than cool. Temperature is uncomfortably low. Cool suggests a pleasantly low temperature; as-

• I can't stand this cold wave.
• A nice cool breeze is blowing.

Hot, likewise suggest a higher temperature than warm. It is often uncomfortable. But warm is a pleasantly high temperature; as-

• You can't work long hours on a hot day.
• It was warm, but not hot, day before yesterday.