  The resummed thermodynamics of ${\cal N}=4$ supersymmetric Yang-Mills theory
in four space-time dimensions ($\text{SYM}_{4,4}$) has been calculated
previously to two loop order within hard thermal loop perturbation theory
(HTLpt) using the canonical dimensional regularization (DRG) scheme. Herein, we
revisit this calculation using the regularization by dimensional reduction
(RDR) scheme. Since the RDR scheme manifestly preserves supersymmetry it is the
preferred scheme, however, it is important to assess if and by how much the
resummed perturbative results depend on the regularization scheme used.
Comparing predictions for the scaled entropy obtained using the DRG and RDR
schemes we find that for $\lambda \lesssim 6$ they are numerically very
similar. We then compare the results obtained in both schemes with the strict
perturbative result, which is accurate up to order $\lambda^2$, and a
generalized Pad\'{e} approximant constructed from the known large-$N_c$ weak-
and strong-coupling expansions. Comparing the strict perturbative expansion of
the two-loop HTLpt result with the perturbative expansion to order $\lambda^2$,
we find that both the DRG and RDR HTLpt calculations result in the same
scheme-independent predictions for the coefficients at order $\lambda$,
$\lambda^{3/2}$, and $\lambda^2 \log\lambda$, however, at order $\lambda^2$
there is a residual regularization scheme dependence.
