Prayers to Vedic and post Vedic Gods in Valmiki Ramayana.
All Hindu devotees believe that the first book which was written after the Vedas was Valmiki Ramayana. That is why it is called Adhi Grantha.. According to legends Vedas were only codified and written down by Veda Vyasa who was the great grand son of Vasishta (who lived in the Ramayana period). That would mean the book written by Valmiki might have been written down earlier to Vedas and that is why Valmiki’s book is called Adhi Grantha .
Vedas worshipped Gods such as Purusha , Rudra, Shakthi,Brahma ,Yama, Indra , Agni , Surya, Chandra, Vayu , Bhaga , Nakshtras. Purusha(Masculine being) was possibly later identified as Lord Vishnu , Rudra (the angry one) was identified as Lord Shiva(peace) , Shakthi (the power) was latter identified as the feminine principle of Gods , Brahma remained as Brahma the creator , Yama identified as God of death , Indra identified as king of Devas , Surya(sun) , Chandra (moon) , Vayu (wind) , Agni (fire) Bhaga(The god of luck) and Nakshatras as stars. The Vedas were compiled by great sages who taught them to their disciples as spoken word (possibly they did not have alphabets or they thought Since for proper import of Vedic Suthras correct pronunciation was important ) and later passed on them to their disciples to be similarly passed on to their disciples . Possibly because they were transferred as spoken word , they were called as Sruthi (what was heard) . In Vedas some Puranic kings like Janaka , Kaushika etc are also mentioned. Vedas worshipped Gods and made offerings to them through fire. AS an addendum to Vedas were the philosophical works called Upanishads. To the best of my knowledge (limited) there are no temples mentioned in the Vedas . Also added to the Vedas were the Grihya suthras , which defined the rituals that should be performed by an Individual. If you properly analyze the daily rituals prescribed , there also the worship is restricted to various Vedic Gods , except possibly in few places where some names of Lord Vishnu are mentioned .(Eg in Aachamana and in prayers in the last concluding part) .Most of the prayers are addressed to Sun God, Yama, Gayathri etc. Normally these rituals are nowadays restricted to men but in Valmiki Ramayana , Hanuman searches for Sita in river banks in the hope that she would come there to worship in the dusk.
When such is being the case the Fist book of Hinduism (possibly written even earlier to Vyasa giving a written compilation of Vedas ) does not mention about any temples, but some Gods do find mention . Lord Brahma was worshipped by the Asuras by doing penance and not by going to temple . (No stotra there? ) .The Devas are supposed to have approached Lord Vishnu who took incarnation as Rama. Even prayers are very few in Ramayana. Sita while crossing Ganga prays to the river for her safe return.Lord Hanuman when he is not able to find Sita does prays Gods which includes Rama .
“My salutations to Sri Rama along with his brother Lakshmana, My salutations to Sita who is the daughter of Janaka, My salutations to Rudra, Indra, Yama the god of death, Vayu the god of wind, moon, sun and The people of Maruth”, he saluted ( Sundara Kanda/Valmiki Ramayana 13. 63)
Sita prays to the fire God not to hurt Hanuman :-
That broad eyed lady started praying for the welfare of the monkey chief and at that time with great devotion saluted the God of fire and prayed. 53.26
“Supposed I had looked after my husband properly, suppose I had observed the rules of penance properly and if I had thought in my mind of husband only, then be cool to Hanuman.”
“If that great one has little pity on me and not only that if I have at least a bit of luck, then be cool to Hanuman.” 53.28
“Suppose you know me as one as virtuous and only praying always to reach the company of whom who is the soul of justice, then be cool to Hanuman.” 53.29
“If the long armed, truthful and gentleman Sugreeva will help me to cross this danger, then be cool to Hanuman.” 53.30
Later Rama himself was taught Adhithya Hrudayam by sage Agasthya to pray Sun God to get ability to kill Ravana. You do not find Dasaratha praying for a son , nor do we find Rama praying to any God to help locate his wife or when Lakshmana lay killed by Indrajit. This to my mind indicates that praying the post Vedic Gods were still not popular at that time. Prayer, temples , sacred rivers , sacred places all become very common in all books that followed Ramayana.In Bharatha , Bhagawatha and all translations and adaptations of Ramayana all these things became very popular .There are umpteen number of prayers addressed to Rama as God in Adyathma Ramayana.Kamba Ramayana mentions that Lord Ranganatha was the Kula Deivam(clan God) of the solar dynasty and gives a description of several temples visited by Hanuman when he came searching for Sita in the southern direction.