From what I have heard of from my Elders – After 12:00 P.M. Afternoon it will be The Correct Time to Worship Hindu Deceased people (Ancestors & Forefathers) so most of “The Shraddha Ceremonies” will commence from The Afternoons, or “Pitru Tarpan” are given at this Hour, Later “The Madhyahnikam” or Afternoon Worship of The Sun God will be performed by The Brahmins or Priestly Class of people.
In Lord Shiva Temples, since Shiva is also The God of Death & Destruction and also God to The Ghosts, Goblins & Spirits, “Yakshas & Rakshasas” they are said to visit him during Afternoon 12 to 4 P.M. Time period intervals and Worship Lord Shiva in that Time exclusively.
Hence Most Temples will be Shut during afternoons in South India, after they perform a “Mahanaivedyam” or Food Offering to a God or Goddess and “Darshan” to Devotees and Pilgrims will usually be forbidden due to this reason.
It might Differ in Different Parts of India, and in Different Temples with Different Traditions & Techniques of Worship, it might Vary vastly from One Region to another. So I cannot say with Conviction that this Rule will Apply to All or be Correct for All cases.
Please let me know if you know more information on this topic, drop your comments in my inbox or email.