Hi Nicolas -
We develop using Thematic quite a lot, so I am interested in seeing if I can help you get to the bottom of this. It may be the specific "flavor" of the caching plugin you are using. We use W3 Total Cache, and I don't think the same problem results. Learn about this plugin here: http://www.w3-edge.com/wordpress-plugins/w3-total-cache/
But if that is the same plugin you use (there are others with similar names), then take a look at one of our client's sites where we have it in use: http://bfgl.com
If I look at page source for that site, I see:
<body class="wordpress blogid-1 y2011 m12 d31 h22 home singular slug-home page pageid-159 page-author-webfadds page-comments-closed page-pings-closed page-template page-template-NoTitlepage-php mac firefox ff1">
Is this what you did not like? It is actually a very powerful way to take control of what displays on different pages, templates, and even in different browsers. Since each browser gets a class assignment, you could show a different background to people using different browsers, for example, using CSS.
This is not due to W3 Total Cache... these classes are available even without it.