Thermal energy can be conducted by different mechanisms including by single particles or collective excitations. Thermal conductivity is system-specific and shows a richness of behaviors currently explored in different systems including insulators, strange metals and cuprate superconductors. Here, we show that despite the seeming complexity of thermal transport, the thermal diffusivity $alpha$ of liquids and supercritical fluids has a lower bound which is fixed by fundamental physical constants for each system as $alpha_m=frac{1}{4pi}frac{hbar}{sqrt{m_em}}$, where $m_e$ and $m$ are electron and molecule masses. The newly introduced elementary thermal diffusivity has an absolute lower bound dependent on $hbar$ and the proton-to-electron mass ratio only. We back up this result by a wide range of experimental data. We also show that theoretical minima of $alpha$ coincide with the fundamental lower limit of kinematic viscosity $ u_m$. Consistent with experiments, this points to a universal lower bound for two distinct properties, energy and momentum diffusion, and a surprising correlation between the two transport mechanisms at their minima. We observe that $alpha_m$ gives the minimum on the phase diagram except in the vicinity of the critical point, whereas $ u_m$ gives the minimum on the entire phase diagram.
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