We present the results of spectroscopic investigations of the plasma of the pulsed discharge in the capillary with the ablation wall made of a carbon-containing polymer, at the pulse energy 50-150 J, the current 50-120 A, and the discharge pulse duration of 9 ms. The system of video registration and fast spectral diagnostics makes it possible to investigate the spatiotemporal evolution of the plasma structure and parameters both inside the capillary volume (1-2 mm in diameter, 3-5 mm in depth) and in the subsonic plasma jet. On the basis of the 2D-matrix high resolution spectra containing the H-alpha and the H-beta lines, the CN and the Swan molecular bands, and the CuI lines, we obtain the spatiotemporal distributions of the electron density and the plasma temperature in the capillary and the subsonic plasma jet. We reveal the peculiarities of the spatial distribution of the electron density and of the spectral components intensity within both above zones conditioned, in particular, by achievement, in the hot central zone, of an electron temperature above the normal temperature (equal to 16500 K for the H-beta). We analyze the thermodynamic state of the "hot" discharge core and show the possibility of its representation as a highly ionized atmospheric pressure hydrogen plasma.