There is nothing built-in. You could as Anna mentioned build an extension that would allow to send it. There area few ways you could approach this, I have seen in the past an extension that changes the order status which triggers an email based upon the assigned status.
Alternatively you could use Objective HTML's PostMaster add-on. You would need to setup a parcel based upon the rules you want to trigger an email. Once the rule is triggered it will send the email out, the nice thing about this is that you can configure multiple parcels to send out multiple emails or different emails based upon what the user purchased.
The other option and an option that I see a lot of people use is to sign the user up to a MailChimp or CampaignMonitor list that will send out emails a set amount of days from being added to the list. This can be super handy if you have multiple emails that need to be sent out at certain times. The downside to this is that it is not as easy to pull in the purchased items to the email body.