We study freely decaying quantum turbulence by performing high resolution numerical simulations of the Gross-Pitaevskii equation (GPE) in the Taylor-Green geometry. We use resolutions ranging from $1024^3$ to $4096^3$ grid points. The energy spectrum confirms the presence of both a Kolmogorov scaling range for scales larger than the intervortex scale $\ell$, and a second inertial range for scales smaller than $\ell$. Vortex line visualizations show the existence of substructures formed by a myriad of small-scale knotted vortices. Next, we study finite temperature effects in decaying quantum turbulence by using the stochastic Ginzburg-Landau equation to generate thermal states, and then by evolving a combination of these thermal states with the Taylor-Green initial conditions under the GPE. We use finite temperature GPE simulations to extract mean free path by measuring the spectral broadening in the Bogoliubov dispersion relation that we obtain from the spatio-temporal spectra, and use it to quantify the effective viscosity as a function of the temperature. Finally, we perform low Reynolds number simulations of the Navier-Stokes equations, in order to compare the decay of high temperature quantum flows with their classical counterparts, and to further calibrate the estimations of the effective viscosity (based on the mean free path computations).