A new two-dimensional (2D) carbon allotrope, Hexa-C20, composed of C20 fullerene is proposed. State-of-the-art first principles calculations combined with solving the linearized phonon Boltzmann transport equation confirm that the new carbon structure is not only dynamically and thermally stable, but also can withstand temperatures as high as 1500 K. Hexa-C20 possesses a quasi-direct band gap of 3.28 eV, close to that of bulk ZnO and GaN. The intrinsic lattice thermal conductivity κlat of Hexa-C20 is 1132 W m-1 K-1 at room temperature, which is much larger than those of most carbon materials such as graphyne (82.3 W m-1 K-1) and penta-graphene (533 W m-1 K-1). Further analysis of its phonons uncovers that the main contribution to κlat is from the three-phonon scattering, while the three acoustic branches are the main heat carriers, and strongly coupled with optical phonon branches via an absorption process. The ultrahigh lattice thermal conductivity and an intrinsic wide band gap make the Hexa-C20 sheet attractive for potential thermal management applications.