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Two-dimensional (2D) polymers are organic analogues of graphene. Compared to graphene, 2D polymers offer a higher degree of tunability in regards to structure, topology, and physical properties. The thermal transport properties of 2D polymers play a crucial role in their applications, yet remain largely unexplored. Using the equilibrium molecular dynamics method, we study the in-plane thermal conductivity of dubbed porous graphene that is comprised of π-conjugated phenyl rings. In contrast to the conventional notion that π-conjugation leads to high thermal conductivity, we demonstrate, for the first time, that π-conjugated 2D polymers can have either high or low thermal conductivity depending on their porosity and structural orientation. The underlying mechanisms that govern thermal conductivity were illustrated through phonon dispersion. The ability to achieve two orders of magnitude variance in thermal conductivity by altering porosity opens up exciting opportunities to tune the thermal transport properties of 2D polymers for a diverse array of applications.