The long-term evolution of the mantle is simulated using spherical annulus geometry to examine the effect of heterogeneous thermal conductivity on the stability of reservoirs of primordial material. Often in numerical models, purely depth-dependent profiles synthesize the mean conductivities of mantle materials at their respective conditions in-situ. However, because conductivity also depends on temperature and composition, the effects of these dependencies on mantle conductivity are masked. This issue is significant because dynamically evolving temperature and composition introduce lateral variations in conductivity, especially in the deep mantle. Our simulations allow assessing the consequences of these variations on mantle dynamics, in combination with the reduction in piles' conductivity due to its expected high temperatures and enrichment in iron, which has so far not been well examined. We find that when lowermost mantle conductivity is comparable to low end-member estimates (due to strong temperature dependence or weak depth dependence), the imparted thermal buoyancy (from heat-producing element enrichment) destabilizes the reservoirs and influences core�mantle boundary coverage configuration and the onset of dense material entrainment. Furthermore, composition dependence of conductivity only plays a minor role that behaves similarly to a small conductivity reduction due to temperature. Nevertheless, this effect may be amplified when depth dependence is increased. For the cases we examine, when the lowermost mantle�s mean conductivity is greater than twice the surface conductivity, reservoirs can remain stable for very long periods of time, comparable to the age of the Earth.