Hello Arsenijs,
When you say header fonts I assume you are talking about headings? if so, you must know that those headings are handled by JavaScript and Cufon, so you may need to remove the code.
1. Open header.php with your favorite text editor.
2. Remove the code from lines 57 to 61.
<script type="text/javascript" src="<?php bloginfo('template_directory'); ?>/js/cufon-yui.js"></script>
<script type="text/javascript" src="<?php bloginfo('template_directory'); ?>/js/Anivers_400.font.js"></script>
<script type="text/javascript">
Cufon.replace('h1, h2, h3, h4, h5, h6');
</script>
And you should be good to go =)
Please let me know if you require further assistance.
Best regards,
Helios.