  The relative entropy between very high energy localized excitations and the
vacuum, where both states are reduced to a spatial region, gives place to a
precise definition of a local temperature produced by vacuum entanglement
across the boundary. This generalizes the Unruh temperature of the Rindler
wedge to arbitrary regions. The local temperatures can be read off from the
short distance leading terms in the modular Hamiltonian. For free scalar and
fermion fields they have a universal geometric expression that follows by
solving a particular eikonal type equation in Euclidean space. This equation
generalizes to any dimension the holomorphic property that holds in two
dimensions. For regions of arbitrary shapes the local temperatures at a point
are direction dependent. We compute their explicit expression for the geometry
of a wall or strip.
