This is an area I have addressed quite a bit over the years, there's no absolute right answer of course so all I can do is say how I've approached it.
Firstly, I agree with Phil in that I have always tried to adapt the 5 working days approach, I also like the "3 strikes" rule, in that user gets an email at resolution with relevant fix details but also with a notification of the cooling off period and that after that if the provider does not hear from them then a new ticket would need to be logged. After 3 days they get a gentle reminder of the move to closure in a further 2 days and then after the 5th day the system sets the status to closed (I would not email the user again). This approach does depend on your customers/users appetite for email and how they perceive communication from their provider at present (too much, about right, too little).
I would also say that you need to have someone with the role/system privilege to overwrite the cool off rule (I would say typically this would be your Svc Desk Manager), the reason I say that is that there will also be situations that drive process exceptions or relationship reasons whereby you may wanted to take the decision due to circumstances to re-open a call in a closed state (the challenge is ensuring this is the exception not the rule!).
Lastly, I would recommend that the resolution, cool off to closure timeframe and activity is clearly documented and agreed in your SLA's.
Hope this helps!