Motivated by recent advances in the synthesis of pentagonal covalent organic frameworks (penta-COFs) and the experimental realization of twisted COF bilayers, we present a theoretical investigation into the thermal transport properties of these synthesized materials and their twisted bilayer counterparts. Based on molecular dynamics simulations, we show that monolayer penta-COFs exhibit ultralow in-plane thermal conductivities as low as 0.44 W·m-1·K-1 at 300 K with an exceptionally weak temperature dependence due to the strongly localized phonon vibrational modes in the strained linkers and vertices, which contribute minimally to the thermal transport. More interestingly, introducing interlayer twisting slightly enhances the in-plane thermal conductivities, increasing from 0.41 ± 0.01 to 0.48 ± 0.02 W·m-1·K-1 at 300 K as the twist angle decreases from 36.87° to 16.26°, yielding twist-tolerant behavior. This contrasts with the commonly observed suppression trends in twisted atom-based bilayers. Further detailed analysis of the spatial and time-resolved vibrational characterizations reveals that this behavior results from a competition between the twist-induced moiré disorder that typically suppresses thermal transport and the structural recoupling facilitated by the intrinsic porosity and flexibility of the organic skeletons that enhances phonon transport. These findings deepen the fundamental understanding of the thermal transport properties of penta-COFs, which are distinct from those of atom-based materials.