Lord Vishnu ,from the Vedic stand point, is a form of Narayana,who is a manifestation of Purusha.
Vishnu is the Protector, the word Vishnu is from the Sanskrit word ‘Jishnu’, that which sustains.
His forms are many ,so are His Avatars, numbering 10/12.
The Vishnu Sahasranama calls Him as,
‘Chaturmurthi,Chatur Bahu’, Chatur Vyuha, Chatur Gathi ‘four headed, with four arms, four manifestations, and four Goals.
I was curious to find out the reference as one normally sees Vishnu with One head and Four arms.
The first reference of Vishnu with Head appears in the Mahabharata.
Though I am unable to locate any temple associated with this form., there are Temples in Kashmir with this Icon.
If there is any temple or the Icon is known to some people, please send in the information.
The Four Heads represent ,
Varaha, the Boar Avatar,
and Kapila ,representing Ferociousness or Asura Bhava.
This is one interpretation.
My view is that as Sage Kapila, the Founder of Samkhya System of Indian Philosophy, is an Avatar of Vishnu, the fourth face may represent him.
Pancharatra system explains thus,
Vasudeva (Krishna), Samkarshana (Balarama), Pradyumna and Aniruddha – four vyuhas (manifestations) of Vishnu.