  Continued improvement of heat control in mesoscopic conductors brings novel
tools for probing strongly correlated electron phenomena. Motivated by these
advances, we comprehensively study transport due to a temperature bias in a
quantum point contact device in the fractional quantum Hall regime. We compute
the charge-current noise (so-called delta-$T$ noise), heat-current noise, and
mixed noise and elucidate how these observables can be used to infer strongly
correlated properties of the device. Our main focus is the extraction of
so-called scaling dimensions of the tunneling anyonic quasiparticles, of
critical importance to correctly infer their anyonic exchange statistics.
