  The noncentrosymmetric ClO$_4$ anions of the organic superconductor
(TMTSF)$_2$ClO$_4$ order below 24K. The size of domains where the anions are
ordered is substantially dependent on the cooling rate which is a key parameter
for the stability of the low temperature electronic ground states. We study the
effect of the cooling rate on the SC phase within a self consistent approach in
the framework of the time dependent Ginzburg-Landau theory taking into account
the superconducting fluctuations. We derive the superconducting transition
temperature which is found to decrease with increasing cooling rate in
agreement with recent experimental data.
