wp_get_http has been deprecated. Use WP_Http instead

I use a premium plugin (for theme dev.) that has included the WordPress Importer plugin and I get a deprecated notice:

"wp_get_http has been deprecated. Use WP_Http instead"

But the WP_Http send me to this function.

The question is how to use wp_http_supports in the following code instead of wp_get_http:

function fetch_remote_file( $url, $post ) {
    // extract the file name and extension from the url
    $file_name = basename( $url );

    // get placeholder file in the upload dir with a unique, sanitized filename
    $upload = wp_upload_bits( $file_name, 0, '', $post['upload_date'] );
    if ( $upload['error'] )
        return new WP_Error( 'upload_dir_error', $upload['error'] );

    // fetch the remote url and write it to the placeholder file
    $headers = wp_get_http( $url, $upload['file'] );

    // request failed
    if ( ! $headers ) {
        @unlink( $upload['file'] );
        return new WP_Error( 'import_file_error', __('Remote server did not respond', 'wordpress-importer') );
    }

    // make sure the fetch was successful
    if ( $headers['response'] != '200' ) {
        @unlink( $upload['file'] );
        return new WP_Error( 'import_file_error', sprintf( __('Remote server returned error response %1$d %2$s', 'wordpress-importer'), esc_html($headers['response']), get_status_header_desc($headers['response']) ) );
    }

    $filesize = filesize( $upload['file'] );

    if ( isset( $headers['content-length'] )  $filesize != $headers['content-length'] ) {
        @unlink( $upload['file'] );
        return new WP_Error( 'import_file_error', __('Remote file is incorrect size', 'wordpress-importer') );
    }

    if ( 0 == $filesize ) {
        @unlink( $upload['file'] );
        return new WP_Error( 'import_file_error', __('Zero size file downloaded', 'wordpress-importer') );
    }

    $max_size = (int) $this-max_attachment_size();
    if ( ! empty( $max_size )  $filesize  $max_size ) {
        @unlink( $upload['file'] );
        return new WP_Error( 'import_file_error', sprintf(__('Remote file is too large, limit is %s', 'wordpress-importer'), size_format($max_size) ) );
    }

    // keep track of the old and new urls so we can substitute them later
    $this-url_remap[$url] = $upload['url'];
    $this-url_remap[$post['guid']] = $upload['url']; // r13735, really needed?
    // keep track of the destination if the remote url is redirected somewhere else
    if ( isset($headers['x-final-location'])  $headers['x-final-location'] != $url )
        $this-url_remap[$headers['x-final-location']] = $upload['url'];

    return $upload;
}

Any help will be greatly appreciated. Thanks.