We study properties of thermal transport and quantum many-body chaos in a lattice model with $Ntoinfty$ oscillators per site, coupled by strong nonlinear terms. We first consider a model with only optical phonons. We find that the thermal diffusivity $D_{rm th}$ and chaos diffusivity $D_L$ (defined as $D_L = v_B^2/ lambda_L$, where $v_B$ and $lambda_L$ are the butterfly velocity and the scrambling rate, respectively) satisfy $D_{rm th} approx gamma D_L$ with $gammagtrsim 1$. At intermediate temperatures, the model exhibits a ``quantum phonon fluid regime, where both diffusivities satisfy $D^{-1} propto T$, and the thermal relaxation time and inverse scrambling rate are of the order the of Planckian timescale $hbar/k_B T$. We then introduce acoustic phonons to the model and study their effect on transport and chaos. The long-wavelength acoustic modes remain long-lived even when the system is strongly coupled, due to Goldstones theorem. As a result, for $d=1,2$, we find that $D_{rm th}/D_Lto infty$, while for $d=3$, $D_{rm th}$ and $D_{L}$ remain comparable.
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