Ancient Greek gods and goddesses did not think theaters were temples, although some archeologists might have made such assumptions. Gods of music, dance and education in the arts included Apollo and Artemis, the former presiding over music and poetry, and the latter over the choirs and dances of girls. Other important musical gods included the nine Muses, the dancing Charites or Graces, and the musical demi-gods Hymenaeus and Linos. Dionysus, Hermes and Aphrodite were also gods of music and the arts.
You have not mentioned which god. Theatrical performances were don in honour of the gods but in special theatres, not temples which each were the residences of a particular god.
They were religious festivals in honour of the gods. The were held in cities at appropriate locations - first temples, then special theatres.
Most of the ancient temples and theatres in Greece were built between 575 bc and 300 bc. A few were built before and after that time frame.
In the ancient Greek theatres by the actors.
Dionysus
Ancient Temples such as the Parthenon and the ancient wonder of the world, the statue of Zeus.
The public buildings were the temples and treasury on the Acropolis (high city), and down below the the Agora (market square) and the theatres, and across to the river or sea ports, plus the walls which surrounded and protected the city and ports.
Theatre of Dionysus and Theatre of Herod Atticus
Ancient Greece
Auditoriums, Sculptures, Temples, Theaters and Statues.
In ancient times there were hymns and funeral rites of the dead where he was invoked, he also had temples in ancient Greece.
Aristotle =]]