Word Distinction: Talking About Temperatures

Low Temperatures

Cold suggests a lower temperature than cool, perhaps uncomfortably low:
cold weather
Cool often suggests a pleasantly low temperature:
a nice cool breeze
a lovely cool room (said when you are hot)

High Temperatures

In the same way, hot suggests a higher temperature than warm, or a temperature which would not be comfortable for a long period. Warm often suggests a pleasantly high temperature:
The handle is too hot to touch.
I've caught a cold, so I'm going to take a hot bath and go to bed.
I could lie in a warm bath for hours.
a llvoely warm room (said when you are cold)