There are some conditions and medications that can cause a person to not sweat. It can be quite dangerous and cause heat stroke! http://www.mamashealth.com/skin/anhidrosis.asp

Some people do just naturally turn red when hot though. My mom does. It can be quite startling looking, but its not dangerous. I do to some extent as well - I probably inherited it from her, but I have a more olive skin tone, so it doesn't show as much on me.