There are many ways of going about doing the random image selection.  I am retrieving an image based on the images stored in a particular directory.  I used this regex:

if ( preg_match("/(\.gif|\.jpg|\.png)$/", $img_file) ) {
$images[] = $img_file;
}

to retrieve my images, and

$image = file_get_contents($root . $path . “/” . $img);

to retrieve the actual image.  Now WP Super Cache can still serve up a cached page with http://nathanielengelsen.com/headerimage.php always set as the default header image, but headerimage.php can serve up a random dynamic image with every call.