The modified self-consistent phonon approximation is generalized to calculate the open base pair probability of a (TATA)2 insert between two semi-infinite poly(dA-dC) . poly(dG-dT) helices. An iterative method based entirely on the Green's function method is developed to compute the open interbase hydrogen bond probability of the insert and near bases versus temperature. The open interbase hydrogen bond probability is calculated for two temperatures and compared with perfect homopolymer open base pair probabilities at room temperature. The probability of opening is enhanced by a factor of two for the major groove bond of the AT pair at the transcriptional downstream end of the (TATA)2 insert. The total base pair opening probability of that pair is enhanced by 54%. The probability of the next inline GC base pair to be open is increased by a factor of ten.