I had gotten a new computer pretty recently and synced it up to my old one so that I wouldn't have to set everything up again. I was able to change the thumbnail of my bookmarks on speed dial before, but now it's the default one for the websites.
@spooncultist Go to the website, then click on the heart in the address bar. Use the left and right arrows next to the image to select the thumbnail you prefer. Dismiss the palette by clicking elsewhere when done.