  We compute the first-order $\alpha'$ corrections to a family of
4-dimensional, 4-charge, non-extremal black hole solutions of Heterotic
Supergravity in the case with 3 independent charges. The solutions are fully
analytic, reproduce the extremal limit previously found in the literature and,
applying T-duality, they transform as expected. If we reduce to the case with a
single independent charge we obtain the corrections to four embeddings of the
Reissner-Nordstr\"om black hole in string theory. We completely characterize
the black hole thermodynamics computing the Hawking temperature, Wald entropy,
mass, gauge charges and their dual thermodynamic potentials. We verify that all
these quantities are related by the first law of extended black hole mechanics
and the Smarr formula once we include a potential associated to the
dimensionful parameter $\alpha'$ and the scalar charges. We found that the
latter are not identified with the poles at infinity of the scalar fields
because they receive $\alpha'$ corrections.
