  The structure and composition of simple ices can be modified during stellar
evolution by protostellar heating. Key to understanding the involved processes
are thermal and chemical tracers that can diagnose the history and environment
of the ice. The 15.2 $\mu$m bending mode of $^{12}$CO$_2$ has proven to be a
valuable tracer of ice heating events but suffers from grain shape and size
effects. A viable alternative tracer is the weaker $^{13}$CO$_2$ isotopologue
band at 4.39 $\mu$m which has now become accessible at high S/N with the
$\textit{James Webb}$ Space Telescope (JWST). We present JWST NIRSpec
observations of $^{13}$CO$_2$ ice in five deeply embedded Class 0 sources
spanning a wide range in luminosities (0.2 - 10$^4$ L$_{\odot}$ ) taken as part
of the Investigating Protostellar Accretion Across the Mass Spectrum (IPA)
program. The band profiles vary significantly, with the most luminous sources
showing a distinct narrow peak at 4.38 $\mu$m. We first apply a
phenomenological approach and show that a minimum of 3-4 Gaussian profiles are
needed to fit the $^{13}$CO$_2$ absorption feature. We then combine these
findings with laboratory data and show that a 15.2 $\mu$m $^{12}$CO$_2$ band
inspired five-component decomposition can be applied for the isotopologue band
where each component is representative of CO$_2$ ice in a specific molecular
environment. The final solution consists of cold mixtures of CO$_2$ with
CH$_3$OH, H$_2$O and CO as well as segregated heated pure CO$_2$ ice. Our
results are in agreement with previous studies of the $^{12}$CO$_2$ ice band,
further confirming that $^{13}$CO$_{2}$ is a useful alternative tracer of
protostellar heating events. We also propose an alternative solution consisting
only of heated CO$_2$:CH$_3$OH and CO$_2$:H$_2$O ices and warm pure CO$_2$ ice
for decomposing the ice profiles of the two most luminous sources in our
sample.
