Can’t get image size set with set_post_thumbnail_size() function

They work independently of eachother. You need to call the one you created in the functions.php.

So in your functions.php you would have something like:

if (function_exists('add_theme_support')) {
add_theme_support( 'post-thumbnails' );
set_post_thumbnail_size( 75, 75, true ); // default thumbnail size
add_image_size('my-custom-thumb', 80, 80, true); //custom size
}

and then to call your custom thumbnail you would add this where you want it to appear:

<?php echo the_post_thumbnail('my-custom-thumb'); ?>