  We study a natural generalization of that given in [arXiv:2005.13198
[hep-th]] to heterotic string. Namely, starting from the generic Gepner models
for Calabi-Yau 3-folds, we construct the non-SUSY heterotic string vacua with
the vanishing cosmological constant at the one loop. We especially focus on the
asymmetric orbifolding based on some discrete subgroup of the chiral
$U(1)$-action which acts on both of the Gepner model and the $SO(32)$ or
$E_8\times E_8$-sector. We present a classification of the relevant orbifold
models leading to the string vacua with the properties mentioned above. In some
cases, the desired vacua can be constructed in the manner quite similar to
those given in [arXiv:2005.13198 [hep-th]] for the type II string, in which the
orbifold groups contain two generators with the discrete torsions. On the other
hand, we also have simpler models that are just realized as the asymmetric
orbifolds of cyclic groups with only one generator.
