Understanding the heat flow in polymers is at the onset of many developments in designing advanced functional materials. Here, however, amorphous linear polymers usually exhibit a very low thermal conductivity κ, often hindering their broad applications. In this context, two common routes to increase κ are via semicrystallinity and cross-linking. It can therefore be inferred that the combination of these two effects may result in a further increase of κ with respect to the systems where only one of these two effects is important. Using molecular dynamics simulations, we investigate κ in semicrystalline polymer networks. Contrary to a priori understanding, we show that a combination of cross-linking and crystallinity does not always increase κ. Instead, a delicate competition between the lattice periodicity, the cross-linker types, and the bond density dictates the tunability of κ in these complex macromolecular systems. These results are also compared with the existing experiments.