You can view and download the thumbnail used in a Youtube video by checking the page source and then looking for the "OG Image" Open Graph meta tag.
The "OG Image" meta tag is one of several Open Graph meta-tags that youtube uses to tell social networks like facebook which image to use in-case someone shares/embeds a video in their social network page. In 99% of cases, the "OG Image" tag that youtube uses is the thumbnail of video.
So here are the steps on how to locate the "OG Image" tag and there-by retrieve the URL of the video thumbnail:
Step 1: Open the youtube video in your browser. For this example, I am using the following video:
Note: I am using Firefox as my browser, so the instructions here are specific to Firefox, but this works in Chrome and Internet Explorer as well.
Step 2: Point your cursor on a blank area of the video page.
Step 3: 'Right click' on the blank area and select View Source or View page Source as shown in the image below:
Step 4: On the view source page, do a search (CTRl+F) for the phrase 'og:image'.
Now you should be able to see the thumbnail URL as shown in the image below:
From this tag, the URL of the thumbnail image would be: https://i.ytimg.com/vi/mcixldqDIEQ/maxresdefault.jpg
You can now copy and paste this URL in your browser to view it and then download it if you want.
Step 5: To download the image just right click on the image and click 'Save Image As' and then 'Save' to save it to your computer.