India: A Sacred Geography by Diana L. Eck (2012) is the most useful single volume for understanding why a town like Vemulawada matters. Eck maps the sacred landscape of India — its tirthas, sacred rivers, temple cities — and explains how pilgrimage works as a way of knowing and inhabiting the subcontinent. The concept of "Dakshina Kashi" and the network of Kashi analogues across India is explored in detail.
Nine Lives: In Search of the Sacred in Modern India by William Dalrymple (2009) follows nine individuals living at the intersection of traditional devotion and contemporary India. Several chapters deal directly with Shaivite traditions and temple devotion in south India. Dalrymple writes with deep sympathy and no condescension; reading it before visiting a pilgrimage town changes what you see there.
The Argumentative Indian by Amartya Sen (2005) is not a pilgrimage book, but its essays on Indian pluralism and the tradition of communal coexistence are directly relevant to Vemulawada's unusual character as a temple shared by Hindu and Muslim devotees. Sen's argument that tolerance and debate are as native to Indian culture as piety gives context to what you witness at the temple.
Telangana: The State of Affairs by various contributors — academic and journalistic writing on the formation and character of Telangana as a state, including the cultural and religious geography that distinguishes the region from coastal Andhra. Useful background for understanding why a temple in what was rural Nizam territory grew to such statewide significance.