Hi,
As you say, there is this method with AcyMailing:
www.acyba.com/acymailing/388-automatic-r...s-with-hikashop.html
But that's for unpaid orders. For carts, there is nothing in place.
The mass actions system we have in HikaShop can also be used to send emails for unpaid orders, but nothing for the carts that have not been converted to orders.
Thus it would require development.
If you're a developer, you can do it by creating a plugin of the group hikashop and implement the onHikaCronTrigger (as explained in our developer documentation), and in there, run a MySQL query to load the carts that are linked to customers and modified more than X days ago while no orders being created by the customer in the mean time. And finally, send an email to each user with the content that you want.