  We show there are analogues to the Unruh temperature that can be defined for
any quantum field theory and region of the space. These local temperatures are
defined using relative entropy with localized excitations. We show important
restrictions arise from relative entropy inequalities and causal propagation
between Cauchy surfaces. These suggest a large amount of universality for local
temperatures, specially the ones affecting null directions. For regions with
any number of intervals in two space-time dimensions the local temperatures
might arise from a term in the modular Hamiltonian proportional to the stress
tensor. We argue this term might be universal, with a coefficient that is the
same for any theory, and check analytically and numerically this is the case
for free massive scalar and Dirac fields. In dimensions $d\ge 3$ the local
terms in the modular Hamiltonian producing these local temperatures cannot be
formed exclusively from the stress tensor. For a free scalar field we classify
the structure of the local terms.
