The amplification of the superconducting critical temperature Tc from the low temperature range in homogeneous 2D planes (Tc<23 K) to the high temperature range (23 K<Tc<150 K) in an artificial heterostructure of quantum stripes is calculated. The high Tc is obtained by tuning the chemical potential near the bottom of the nth subband at a shape resonance, in a range, whithin the energy cutoff for the pairing interaction. The resonance for the gap at the nth shape resonance is studied for a free electron gas in the BCS approximation as a function of the stripe width L, and of the number of electrons {rho} per unit surface. An amplification factor for coupling 0.1<{lambda}<0.3 is obtained at the third shape resonance raising the critical temperature in the high Tc range.
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