When you add a \"link\" type post to Tumblr:
...your admin shows a small thumbnail of any image as
This is how it's done:
Click on your blogs name on the dashboard above or in the bloglist on the right hand side.
Click on Customize on the right hand side (or just go to the template you chose)
Once you're in there you can change the HTML on top on the left hand side, right under the templates name and icon
There you look for the
{block:Link}
and before the description you add:
{block:Thumbnail}
<img src="{Thumbnail}" alt="{Name}">
{/block:Thumbnail}`
Tumblr recently added some new theme operators to allow for link thumbnails.
I presume this works the same as video thumbnails work and may only be available if the linked site creates the thumbnail.
{block:Link}
{block:Thumbnail}
<img src="{Thumbnail}" alt="{Name}">
{/block:Thumbnail}
{/block:Link}
Reference: http://www.tumblr.com/docs/en/custom_themes#link-posts