Third harmonic generation (THG) efficiency is shown to be a greatly enhanced at the onset of inelastic scattering of electrons on optic phonons. Scaling experiments are performed on n-type InP at the pump wave frequency of 9.43 GHz at 80 K. Monte Carlo modeling is employed for scaling the effect to the 3(rd) harmonic frequency of 1 THz. The THG efficiency in n-type GaAs and InP as well as in the wurtzite phase of n-type InN and GaN compound crystals is compared to that in n-type Si. The efficiency maximum is found to weaken due to the quasi-elastic scattering on acoustic phonons and elastic scattering on ionized impurities. Nevertheless, the THG efficiency at 1 THz in InP crystals cooled down to liquid nitrogen temperatures is predicted to be 2 orders of magnitude higher than the reference value of 0.1% experimentally recorded up to now in n-type Si.