I havent tested this, but see if this works in customer/main/product.tpl:
Code:
{* // 60 * 60 * 24 * 20 days in unix time = 1728000 *}
{if ($product.add_date gt $smarty.now - 1728000) and ($product.add_date lt $smarty.now)}
[img]{$ImagesDir}/mynew.gif[/img]
{/if}
If you have this showing after the product name inside the main table on the product page the code has to be altered to fit within the dialog code.
All of that is untested, but i am sure it will work.