In this work we consider lateral current pumped GaAs/AlGaAs quantum wells as sources of incoherent terahertz radiation. The lateral field heats the electrons in a two-dimensional quantum layer and increases the population of higher subbands, hence also increasing the radiation power generated in spontaneous intersubband emission processes. Digitally graded quasi-parabolic and simple square quantum wells are considered, and the advantages of both types are discussed. Calculations at lattice temperatures of 77 K and 300 K, for electric fields up to 10 kV / cm, show that the optical output power of ∼100-200 W/ m2 may be achieved for the 7 THz source. The main peak of the spectrum, at 7 THz, of the quasi-parabolic quantum well exceeds the black body radiation at 300 K by approximately a factor of two and by two orders of magnitude at 77 K.