You log into your Etsy account and see that you have something going on in that off-kilter concentric circle button called Activity. You click on it and see someone chose your item to be featured in a treasury. You're excited that someone likes your listing but don't know what to do or how to capitalize on it.
It's easy. You do a lot of the same things you would do if you were marketing your own treasury.
First, you need to click on that treasury. That gives it another view, which helps with its hotness. What's hotness? It's Etsy's nebulous and poorly defined way of organizing what treasuries appear on the top of the list at any given moment. It's essentially a popularity contest driven by people like you.
Second, you need to comment on the treasury. This creates another link to your shop (item is one, your comment is two). Try to say something relevant to the theme of the treasury. If you can't think of anything, compliment on the creator's treasury making skills and/or thank them for including your listing. I'm more likely to click on an interesting comment than another bland bit of fan service.
Third, you need to click on the individual listings. The easy way to do it is to right-click on each item and open it in a new tab. You do this because hotness is also measured by clicks on the items. By opening each item in a new tab, you are giving the treasury 16 more clicks in under a minute.
Fourth, you need to promote your appearance on the treasury. Post it on your Facebook wall, tweet it to your followers, or even post it on your own blog. Whatever you can do to get more people to click, comment, and share the treasury only helps more people see your item representing your shop.
If a treasury becomes popular enough and is on theme for Etsy's Merchandising Desk, it might be put in the daily Etsy Finds e-mails or, better yet, on the front page. That gives you a lot more exposure for your shop for very little work on your own part. It's worth it to try these steps every time you're featured in a treasury.