We present an experimental setup capable of measuring the near DC conductivity of laser generated warm dense matter using single-shot terahertz time-domain spectroscopy. The setup uses a reflective echelon and balanced detection to record THz waveforms with a minimum detectable signal of 0.2% in a single laser pulse. We describe details of the experimental setup and the data analysis procedure and present single-shot terahertz transmission data on aluminum that has been laser heated to an electron temperature of 0.5 eV.