First principles total energy calculations are performed to investigate the Si(001)-(3 x 4) reconstruction induced by the adsorption of group III metals (Ga, Al and In) when deposited at high temperatures. We have considered different models in our study and we have found that the pyramid-like structure proposed by Bunk et al. for In on Si(001) yields the most stable atomic configuration in all cases. We present a detailed description of this surface reconstruction, and compare the structural parameters for Al, Ga and In.