Accurately modeling dense plasmas over wide ranging conditions of pressures and temperatures is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we investigate the thermodynamic, structural, and transport properties of carbon at warm and hot dense matter conditions using ab initio electronic structure methods. In particular, using the spectral quadrature (SQ) method, we report the first such results at the level of Kohn-Sham density functional theory; free of average-atom and/or orbital-free approximations. We carry out ab initio molecular dynamics simulations to calculate the equation of state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities between 8 g/cm 3 and 16 g/cm 3 and temperatures ranging from 100 kK to 10 MK. We find that the computed EOS and Hugoniot are in good agreement with the SESAME database and path integral Monte Carlo results. Additionally, we demonstrate the calculation of the ion-ion structure factor and viscosity for selected points that benefit from the linear and parallel scaling of the SQ method.