  We use spectroscopic data for ${\sim}6,000$ Red Giant Branch (RGB) stars in
the Small Magellanic Cloud (SMC), together with proper motion data from
\textit{Gaia} Early Data Release 3 (EDR3), to build a mass model of the SMC. We
test our Jeans mass modelling method (\textsc{Binulator}+\textsc{GravSphere})
on mock data for an SMC-like dwarf undergoing severe tidal disruption, showing
that we are able to successfully remove tidally unbound interlopers, recovering
the Dark Matter density and stellar velocity anisotropy profiles within our
95\% confidence intervals. We then apply our method to real SMC data, finding
that the stars of the cleaned sample are isotropic at all radii (at 95\%
confidence), and that the inner Dark Matter density profile is dense,
$\rho_{\rm DM}(150\,{\rm pc}) = 2.81_{-1.07}^{+0.72}\times 10^8 M_{\odot} \rm
kpc^{-3} $, consistent with a $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cusp at
least down to 400\,pc from the SMC's centre. Our model gives a new estimate of
the SMC's total mass within 3\,kpc ($M_{\rm tot} \leq 3\,{\rm kpc})$ of
$2.34\pm0.46 \times 10^9 M_{\odot}$. We also derive an astrophysical
\textquote{$J$-factor} of $19.22\pm0.14$\, GeV$^2$\,cm$^{-5}$ and a
\textquote{$D$-factor} of $18.80\pm0.03$\, GeV$^2$\,cm$^{-5}$, making the SMC a
promising target for Dark Matter annihilation and decay searches. Finally, we
combine our findings with literature measurements to test models in which Dark
Matter is \textquote{heated up} by baryonic effects. We find good qualitative
agreement with the Di Cintio et al. 2014 model but we deviate from the Lazar et
al. 2020 model at high $M_*/M_{200} > 10^{-2}$. We provide a new, analytic,
density profile that reproduces Dark Matter heating behaviour over the range
$10^{-5} < M_*/M_{200} < 10^{-1}$.
