  Thermal transport at short length and time scales inherently constitutes a
nonlocal relation between heat flux and temperature gradient, but this is
rarely addressed explicitly. Here, we present a formalism that enables detailed
characterisation of the delocalisation effects in nondiffusive heat flow
regimes. A convolution kernel $\kappa^{\ast}$, which we term the nonlocal
thermal conductivity, fully embodies the spatiotemporal memory of the heat flux
with respect to the temperature gradient. Under the relaxation time
approximation, the Boltzmann transport equation formally obeys the postulated
constitutive law and yields a generic expression for $\kappa^{\ast}$ in terms
of the microscopic phonon properties. Subsequent synergy with stochastic
frameworks captures the essential transport physics in compact models with easy
to understand parameters. A fully analytical solution for $\kappa^{\ast}(x')$
in tempered L\'evy transport with fractal dimension $\alpha$ and diffusive
recovery length $x_{\text{R}}$ reveals that nonlocality is physically important
over distances $\sqrt{2-\alpha} \,\,x_{\text{R}}$. This is not only relevant to
quasiballistic heat conduction in semiconductor alloys but also applies to
similar dynamics observed in other disciplines including hydrology and
chemistry. We also discuss how the previously introduced effective thermal
conductivity $\kappa_{\text{eff}}$ inferred phenomenologically by transient
thermal grating and time domain thermoreflectance measurements relates to
$\kappa^{\ast}$. Whereas effective conductivities depend on the experimental
conditions, the nonlocal thermal conductivity forms an intrinsic material
property. Experimental results indicate nonlocality lengths of 400$\,$nm in Si
membranes and $\simeq 1\,\mu$m in InGaAs and SiGe, in good agreement with
typical median phonon mean free paths.
