  We study delta-T noise -- excess charge noise at zero voltage but finite
temperature bias -- for weak tunneling in 1D interacting systems. We show that
the sign of the delta-T noise is generically determined by the nature of the
dominating tunneling process (more specifically, its scaling dimension). We
clarify the relation between the sign of delta-T noise and the quantum exchange
statistics of tunneling quasiparticles. We find that, for infinite systems
hosting chiral channels with local interactions (e.g., quantum Hall or quantum
spin Hall edges), when the delta-T noise is negative, the tunneling particles
are boson-like, revealing their tendency towards bunching. However, the
opposite is not true: Boson-like particles do not necessarily produce negative
delta-T noise. Importantly, the bosonic nature of particles generating the
negative delta-T is not necessarily intrinsic, but can be induced by the
interactions. This particularly implies that negative delta-T noise for
tunneling between the edge states cannot serve as a smoking gun for detecting
"intrinsic anyons". We also establish a connection between the delta-T noise
and the temperature derivative of the thermal noise in interacting systems,
both governed by the same scaling dimensions. As a demonstration of the above
statements, we study tunneling between two interacting quantum spin Hall edges.
With bosonization and renormalization-group techniques, we find that many-body
interactions can generate negative delta-T noise for both direct tunneling
through a point contact and in Kondo exchange tunneling via a localized spin.
In both setups, we show that the noise can become negative at sufficiently low
temperatures, when interactions renormalize the tunneling to favor boson-like
pair-tunneling of electrons. Our findings show that delta-T noise can probe the
nature of collective excitations in interacting 1D systems.
