We present results on the interaction of hot and cold electrons in a large-area two-dimensional electron-gas-base hot-electron transistor. Four-terminal magnetoresistance measurements of the cold electrons in the two-dimensional electron-gas (2DEG) base, as a function of forward-emitter bias, ${\mathit{V}}_{\mathrm{EB}}$, show significant deviations from the zero-bias condition. We identify two distinct regimes: (i) an enhanced interface scattering as the 2DEG is forced against the collector-barrier heterojunction for low biases before emitter-current injection and (ii) an electron-heating effect in the 2DEG once current injection occurs. We invoke a simple heat-exchange argument to analyze the relaxation of the injected hot carriers.