We present the first experimental measurement of temperature and density of a warm dense plasma produced by a pulsed power driver at the Nevada Terawatt Facility (NTF). In the early phases of discharge, most of the mass remains in the core, and it has been challenging to diagnose with traditional methods, e.g. optical probing, because of the high density and low temperature. Accurate knowledge of the transport coefficients as well as the thermodynamic state of the plasma is important to precisely test or develop theoretical models. Here, we have used spectrally resolved non-collective X-ray Thomson scattering to characterize the dense core region. We used a graphite load driven by the Zebra current generator (0.6 MA in 200 ns rise time) and the Ti He-α line produced by irradiating a Ti target with the Leopard laser (30 J, 0.8 ns) as an X-ray probing source. Using this configuration, we obtained a signal-to-noise ratio ~2.5 for the scattered signal. By fitting the experimental data with predicted spectra, we measured T = 2±1.9 eV, ρ = 0.6±0.5 gr/cc, 70 ns into the current pulse. The complexity of the dense core is revealed by the electrons in the dense core that are found to be degenerate and weakly coupled, while the ions remain highly coupled.