Theme Facet Block Output

I would like to theme the whole Facet container / block. As default the facets are shown as a html-list (<ul>). But for example i want to use a Bootstrap dropdown instead.

I found theme functions within facetapi.theme.inc which i can overwrite. But they are only containing possiblity to cusomize the links within the <li>, but not whole outer (html) part.

For example i would like to change:

<ul class="...">
     <li>1</li>
     <li>2</li>
</ul>

To:

<div class="dropdown ...">
    <div class="item">1</div>
    <div class="item">2</div>
</div>

I would be very thankful if someone could give me a hint how to theme this.
This would also be a great addition to the module to have a theme-file (tpl.php) or at least a theme function which contains the whole wrapper structure.