  Quantum noise has been extensively utilized to investigate various aspects of
quantum transport, such as current-current correlations and wave-particle
duality. A recent focus in this field is on $\Delta_T$ quantum noise, which
arises because of a finite temperature difference at vanishing charge current.
This paper explores the characterization of $\Delta_T$ noise auto-correlation
alongside the shot noise and thermal-noise contributions in a 1D
metal/insulator/superconductor junction. We consider a finite temperature
gradient with zero applied bias for reservoirs at comparable temperatures.
Andreev reflection enhances the $\Delta_T$ noise in a
metal-insulator-superconductor junction in contrast to a metal-insulator-metal
junction in the transparent limit. Unlike quantum noise for which shot-noise
dominates thermal-noise at large bias voltages and finite barrier strength,
$\Delta_T$ thermal-noise is always higher than $\Delta_T$ shot-noise. Thus, a
general bound that is independent of barrier strength is established. This
investigation sheds light on the distinct behavior of $\Delta_T$ noise,
alongside the ratio of shot-noise to thermal-noise contributions, offering
valuable insights into the intricate interplay between finite temperature
gradient, barrier strength, and Andreev reflection.
