When it comes to SEO is it ever a good idea to do a timed (countdown) redirect? For instance: I have a thank you page, but it just seems logical that you would want to redirect the user off that page after a certain amount of time. Will this harm my SEO or is it acceptable?
Since you probably will not be building your thank you page up for SEO purposes then it will not affect your SEO at all.
Where you run into an issue with timed redirects is when dealing with pages that you want people redirected from that once existed (and had SEO value) and you want Google to know that the new page is the defacto replacement for the page that did the 301 redirect so the old pages SEO value is moved to the new page.
In this case Google is probably not going to be ranking your thank you page anyways as it will have low SEO value. If you wanted to you could block Google from crawling the results page with a block for that URL in the robots.txt or by adding a robots meta tag requesting Google not to crawl the page.