Josh does something similar to this. If you know the ID number of the widget in question, you can accomplish this with some custom CSS.
Poke around Josh’s site with Firebug and you can probably figure it out: http://www.joshlobe.com/
He’s using code like this:
#text-11 .widget-title-icon, #text-12 .widget-title-icon {
background: url("http://www.joshlobe.com/wp-content/images/star_add.png") no-repeat scroll 0 0 transparent;
display: block;
float: left;
height: 28px;
margin-left: -10px;
margin-top: -4px;
padding-right: 7px;
width: 28px;
}
It’s pretty cool, actually. I think if you do this, you can leave the widget title blank, or add
#text-11 h3 {
display:none;
}
to hide the title. (Not tested, however.)
To find widget ID’s:
http://blog.kjodle.net/2012/02/24/styling-wordpress-posts-pages-archives-and-home-pages-by-class/