  Motivated by a few preceding papers and a question of R. Longo, we introduce
super-KMS functionals for graded translation-covariant nets over R with
superderivations, roughly speaking as a certain supersymmetric modification of
classical KMS states on translation-covariant nets over R, fundamental objects
in chiral algebraic quantum field theory. Although we are able to make a few
statements concerning their general structure, most properties will be studied
in the setting of specific graded-local (super-) conformal models. In
particular, we provide a constructive existence and partial uniqueness proof of
super-KMS functionals for the supersymmetric free field, for certain subnets,
and for the super-Virasoro net with central charge c>= 3/2. Moreover, as a
separate result, we classify bounded super-KMS functionals for graded-local
conformal nets over S^1 with respect to rotations.
