Please see this thread for an IMHO better solution to this kinda thing: http://wordpress.org/support/topic/209656?replies=11
Note: try the second bit of code that I posted.
If this is not to your liking, you could try the following steps:
First create a directory in your WordPress install directory and put your thumbnail images there. Upload these to your server.
Next come up with a "slug" to use for your image file name. Something like "homepage_thumbnail_filename" would work well.
Next, add a custom field to a post choose "homepage_thumbnail_filename" for the key and type in the name of one of the files in that directory we created in step one. use full name with extension: 'taco_pudding.jpg'
Open the theme file that displays your homepage and type in the following code into your loop:
$img_filename = get_post_meta( $post->ID, 'homepage_thumbnail_filename' , true );
$path_to_img = get_bloginfo( 'url' ) . '/custom_thumbnail_directory/' . $img_filename;
$custom_thumb_img = '<img src="' . $path_to_img . '" alt="" />';
print $custom_thumb_img;
This should work. Let me know what happened...