Not all Gods have a roof over their head. Some Gods sit, stand in the open grassland (still they are designated as temples) to bless the devotees. They are called "Kaaval Theivangal" (Tamil: காவல் தெய்வங்கள்)
This is the frontview of this photo
Village Guardian or patron deity (Kaaval Theivam)
Kallakurichi, Tamil Nadu, India.