Absolute concepts of time and energy are integral to standard thermal physics, but background independent systems are devoid of them. This thesis explores the foundational question of generalising equilibrium statistical mechanics to background independent systems, and applies the resulting formulation to non-perturbative discrete quantum gravity. It offers a discussion of the rich interface of thermal physics and quantum gravity in this context, providing a broad contextualisation of such topics. This work details how standard tools from many-body physics can be generalised to discrete...