How to generate video thumbnails

Is there any way to automatically generate a thumbnail from a YouTube video? I know that YouTube does this on its site, but when I use the embed code and URL on a site, the thumbnail doesn’t show up on the portfolio page, which is where I need it. Right now, it just lists the item’s title with no thumb. You can see this here: site link
I contacted the theme author and he said the theme won’t do it automatically, so I need the easiest possible way to do this – the client is not computer savvy.