  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.
