It is first shown that the thermal fluctuation effects on the transport and on the thermodynamic observables above the superconducting transition may provide, when they are analyzed simultaneously and consistently, a powerful tool to access the relaxation time, tau(0), of the Cooper pairs with wave vector k = 0 in high-temperature cuprate superconductors (HTSC). Then, Ne apply this procedure to optimally doped YBa2Cu3O7-delta (Y-123) crystals. It is found that in this HTSC tau(0) follows, within 20% accuracy, the BCS temperature behaviour and amplitude given by tau(0) = pi h/[8k(B)(T - T-c0)].