© 2017 Author(s). We calculate the thermal conductivity, κ, of the recently synthesized hexagonal diamond (lonsdaleite) Si using first-principles calculations and solving the Boltzmann Transport Equation. We find values of κ which are around 40% lower than in the common cubic diamond polytype of Si. The trend is similar for  Si nanowires, with reductions of the thermal conductivity that are even larger than in the bulk in some diameter range. The Raman active modes are identified, and the role of mid-frequency optical phonons that arise as a consequence of the reduced symmetry of the hexagonal lattice is discussed. We also show briefly that popular classic potentials used in molecular dynamics might not be suited to describe hexagonal polytypes, discussing the case of the Tersoff potential.