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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 temperatureand zero chemical potential. Our final result is ultraviolet finite and allinfrared divergences generated at three-loop level are canceled by summing over$\text{SYM}_{4,4}$ ring diagrams. Non-analytic terms at ${\calO}({\lambda}^{3/2}) $ and $ {\cal O}({\lambda}^2 \log\lambda )$ are generatedby dressing the $A_0$ and scalar propagators. The gauge-field Debye mass $m_D$and the scalar thermal mass $M$ are determined from their correspondingfinite-temperature self-energies. Based on this, we obtain the three-loopthermodynamic functions of $\text{SYM}_{4,4}$ to ${\cal O}(\lambda^2)$. Wecompare our final result with prior results obtained in the weak- andstrong-coupling limits and construct a generalized Pad\'{e} approximant thatinterpolates 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 quantitativelyreliable approximation to the scaled entropy density for $0 \leq \lambda\lesssim 2$.

${\cal N}=4$ supersymmetric Yang-Mills thermodynamics to order $\lambda^2$