As silly as it may sound, I tell my post operative breast augmentation patients to stay away from black bathing suits for a little while until they have healed a bit.    There tends to be numbness around the surgical area and therefore burns CAN occur.  The following article is interesting although I'm having trouble believing there were 3rd degree burns...

Sunbathing NY Woman Suffers Third-Degree Burns After Bikini Overheats 

By New York Post

NEW YORK - A Long Island sun worshiper said she landed in the hospital with third-degree burns on her bust after the under wire in her two-piece bathing suit became superheated, the New York Post reported Sunday.
The black Coco Reef swimsuit had been sitting in her drawer for a while before Robin Corrente, 50, of Yaphank, got the chance to try it out.
She wore it on a 90F (32C) afternoon in August 2008 to soak up some rays in her yard.
"After about an hour, I was hurting," Corrente said. "I went up to take a shower and I realized ... I had a lot of blisters."
A trip to the hospital confirmed she had serious burns, and doctors had to remove a piece of flesh "the size of a dime" from her right breast.
Corrente is suing Coco Reef manufacturer Swimwear Anywhere in Manhattan Supreme Court.
Swimwear Anywhere declined to comment.
Read more: http://www.nypost.com/p/news/