  We analyse the local behaviour of the two-point correlation function of a
quantum state for a scalar field in a neighbourhood of a Killing horizon in a
$2+1$-dimensional spacetime, extending the work of Moretti and Pinamonti in a
$3+1$-dimensional scenario. In particular we show that, if the state is of
Hadamard form in such neighbourhood, similarly to the $3+1$-dimensional case,
under a suitable scaling limit towards the horizon, the two-point correlation
function exhibits a thermal behaviour at the Hawking temperature. Since the
whole analysis rests on the assumption that a Hadamard state exists in a
neighbourhood of the Killing horizon, we show that this is not an empty
condition by verifying it for a massive, real scalar field subject to Robin
boundary conditions in the prototypic example of a three dimensional black hole
background: the non-extremal, rotating BTZ spacetime.
