  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
$\alpha_m=\frac{1}{4\pi}\frac{\hbar}{\sqrt{m_em}}$, 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 $\nu_m$. 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 $\nu_m$ gives the minimum on the entire phase diagram.
