The dimensional reduction of the effective ten-action [Formula: see text] of the heterotic superstring theory to the physical four-action S[gij] results in the appearance of three moduli B(a), whose real parts [Formula: see text], set equal for simplicity, define the radius and shape of the compact internal six-space [Formula: see text], in addition to the dilaton [Formula: see text], the ten-interval being [Formula: see text]. These scalar fields are massless at tree level and can be put into canonical form with coefficients [Formula: see text] for the positive kinetic-energy terms, when higher-derivative terms are ignored, as found by Witten, so that [Formula: see text]. Previously, we have shown that σA and σB acquire a potential from the higher-derivative terms [Formula: see text] and [Formula: see text], which becomes large close to the Planck era. Here, we discuss the renormalization of the kinetic-energy terms due to [Formula: see text] which, after diagonalization, results in a mixing of ∇σB with ∇σA, while the remaining coefficient of (∇σB)2 vanishes at t c ≈ t P /12 in a radiation-dominated Universe, corresponding to a temperature T c ≈ 5 × 1017 GeV , where the four-theory is still classical. At earlier times, the energy is unbounded from below, signalling that the four-theory has become unphysical, and that the string must still be in its uncompactified form with one dilaton ϕ, whose canonical kinetic energy is positive in the Einstein metric. This mechanism depends upon the equation of state of the source for the Friedmann expansion assumed, and is only effective for values of the adiabatic index in the range 1.14 < γ < 2.63, which thus includes radiation (γ = 4/3) and the Zel'dovich equation of state (γ = 2).