We describe a new type of terahertz (THz) detector for astronomical observation using a two-dimensional electron gas (2DEG) as the absorbing medium. The detection principle is based on the hot electron effect in 2DEGs. Electrons are heated by THz radiation and the electron temperature is read out by two symmetrical superconductor - 2DEG tunnelling junctions. Hot electrons are removed via tunnelling through a barrier into the superconducting contacts. The energy gap in the superconducting contacts prevents the escape of the colder, non-photoexcited electrons from the 2DEG. The high mobility 2DEG itself is created within AlGaAs/GaAs heterostructure with a single quantum well. In this paper we present low temperature DC measurements of 2DEG detectors, and measurements of the electron-phonon thermal conductivity of a 2DEG at 4.2 K and 300 mK as a function of electron temperature and magnetic field (in the 4.2 K case). From these measurements we estimate the noise equivalent power (NEP) of an element in a filled array of S-2DEG-S detectors at 4.2 K to be on the order of ≈ 10-14W/√Hz with a response time of ≈ 1ns; at 300 mK, an NEP on the order of ≈ 10-19W/√Hz and a response time of ≈ 0.1μs. Using measured parameters for the normal resistance of the S-2DEG-S contacts, we calculate the effect of using a voltage bias to cool the electrons in the absorber to significantly below a 300 mK base temperature. In this configuration. S-2DEG-S detectors can achieve sufficient sensitivity to detect individual THz photons.