Currently, email templates that are set up in a Thon HQ do not carry over to the next event like the Address Book does.  Even if the participant chooses to Autofill and use the same username/password, they will have to recreate the email templates in their HQ.

Or, if the previous event is still Active, they can log into the old event, copy the text they created and then paste it into the new event's Participant HQ.