Here's how the trust to construct and run the Ram temple could function

There is speculation that the trust to construct and run the Ram temple in Ayodhya will be constituted on the basis of the laws that govern the trust for Jammu’s Mata Vaishno Devi Shrine Board or Gujarat’s Somnath temple. A look into how the Mata Vaishno Devi Shrine Board is run:

The Board was set up in 1986 to manage the upkeep of the temple, and currently also runs a university and a hospital. The Amarnath Shrine Board, set up in 2000, is also based on the Vaishno Devi board
 

The Jammu and Kashmir governor is the ex-officio chairman of the board, which has 10 members. It is run by an IAS officer