W3C recomends to use divs for the style and h1, h2 for the brief titles of the sections, subsections...
Anyway it is allowed to use class in h1, h2.. elements, so under my point of view you can give style to the h elements.
Other subject is to put block's inside the h elements that will be consider as other information block, and that's not a brief title, so that's the reason validators will complain ( I think ).