  The intersection of thermodynamics, quantum theory and gravity has revealed
many profound insights, all the while posing new puzzles. In this article, we
discuss an extension of equilibrium statistical mechanics and thermodynamics
potentially compatible with a key feature of general relativity, background
independence; and we subsequently use it in a candidate quantum gravity system,
thus providing a preliminary formulation of a thermal quantum spacetime.
Specifically, we emphasise on an information-theoretic characterisation of
generalised Gibbs equilibrium that is shown to be particularly suited to
background independent settings, and in which the status of entropy is elevated
to being more fundamental than energy. We also shed light on its intimate
connections with the thermal time hypothesis. Based on this we outline a
framework for statistical mechanics of quantum gravity degrees of freedom of
combinatorial and algebraic type, and apply it in several examples. In
particular, we provide a quantum statistical basis for the origin of covariant
group field theories, shown to arise as effective statistical field theories of
the underlying quanta of space in a certain class of generalised Gibbs states.
