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Classical T Tauri stars (CTTSs) drive strong outflows with temperatures from about 103 K up to a few 106 K. These outflows regulate the angular momentum balance and are therefore tightly related to the accretion process. However, the outflow driving and heating mechanisms are not well understood. We present new HST data of the “prototypical” jet-driving CTTS DG Tau tracing the low-temperature outflow with fluorescently excited far-UV molecular hydrogen emission and the high-temperature part with C IV emission. We find that the spatial distribution of the low-temperature plasma is V-shaped consistent with molecular disk-wind models. Low-velocity shocks (vshock ~ 30 km s−1 ) are probably the pumping source for the FUV H 2 lines. The hot plasma (T > 105 K) is located close to the jet axis at a distance of 40 AU from the driving source and spatially offset from standard (optical) jet-tracers like [S II] or [O I]. It does not show any hints for proper-motion contrasting typical jet properties. The high-temperature plasma is unlikely caused by a hot stellar wind and we propose that the stationary heating is caused by internal shocks or magnetic reconnection.