The diversity of the electronic properties of carbon makes it of key interest to the material science community; nowhere is this more evident than in the myriad potential applications of structured allotropes like grapheme and nano tubes. By contrast, at the high pressures typical of planetary and stellar interiors, the behavior of carbon is poorly understood with large uncertainties in the conductivity and even the material phase. There is growing evidence of the abundance of diamond in the interiors of the ice giant planets Uranus and Neptune; the conductivity of which could potentially influence models for the origin of the unusual magnetic fields of these planets. In laboratory experiments, practical issues with gradients in the temperature and densityof shock compressed matter have hindered accurate measurement and further from distinguishing theoretical models. Here, we present spatially resolved x-ray scattering experiments using LCLS free electron laser to examine and understand the gradients of thermal properties under dynamic shock loading. We employed curved mosaic and perfect imaging crystals. Compared with hydro-dynamic simulations, we present time-resolved data on plasmon dispersion, axial compression gradients and finally carbon melting at shock coalescence.