  We derive exact, asymptotically flat black hole solutions of Einstein-scalar
gravity sourced by a non trivial scalar field with $1/r$ asymptotic behaviour.
They are determined using an ansatz for the scalar field profile and working
out, together with the metric functions, the corresponding form of the scalar
self-interaction potential. Near to the singularity the black hole behaves as
the Janis-Newmann-Winicour-Wyman solution. We also work out a consistent
thermodynamical description of our black hole solutions. For large mass our
hairy black holes have the same thermodynamical behaviour of the Schwarzschild
black hole, whereas for small masses they differ substantially from the latter.
