The role of flux-limited thermal conduction on the fusion performance of the uniaxially driven targets studied by Derentowicz et al. [J. Tech. Phys. 18, 465 (1977) and J. Tech. Phys. 25, 135 (1977)] is explored as part of a wider effort to understand and quantify uncertainties in inertial confinement fusion (ICF) systems sharing similarities with First Light Fusion's projectile-driven concept. We examine the role of uncertainties in plasma microphysics and different choices for the numerical implementation of the conduction operator on simple metrics encapsulating the target performance. The results indicate that choices that affect the description of ionic heat flow between the heated fusion fuel and the gold anvil used to contain it are the most important. The electronic contribution is found to be robustly described by local diffusion. The sensitivities found suggest a prevalent role for quasi-nonlocal ionic transport, especially in the treatment of conduction across material interfaces with strong gradients in temperature and conductivity. We note that none of the simulations produce neutron yields that substantiate those reported by Derentowicz et al. [J. Tech. Phys. 25, 135 (1977)], leaving open future studies aimed at more fully understanding this class of ICF systems.