  We calculate the resummed perturbative free energy of ${\cal N}=4$
supersymmetric Yang-Mills in four spacetime dimensions ($\text{SYM}_{4,4}$)
through second order in the 't Hooft coupling $\lambda$ at finite temperature
and zero chemical potential. Our final result is ultraviolet finite and all
infrared divergences generated at three-loop level are canceled by summing over
$\text{SYM}_{4,4}$ ring diagrams. Non-analytic terms at ${\cal
O}({\lambda}^{3/2}) $ and $ {\cal O}({\lambda}^2 \log\lambda )$ are generated
by dressing the $A_0$ and scalar propagators. The gauge-field Debye mass $m_D$
and the scalar thermal mass $M$ are determined from their corresponding
finite-temperature self-energies. Based on this, we obtain the three-loop
thermodynamic functions of $\text{SYM}_{4,4}$ to ${\cal O}(\lambda^2)$. We
compare our final result with prior results obtained in the weak- and
strong-coupling limits and construct a generalized Pad\'{e} approximant that
interpolates between the weak-coupling result and the large-$N_c$
strong-coupling result. Our results suggest that the ${\cal O}(\lambda^2)$
weak-coupling result for the scaled entropy density is a quantitatively
reliable approximation to the scaled entropy density for $0 \leq \lambda
\lesssim 2$.
