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We analyse fluctuations about $T_c$ in the specific heat of(Y,Ca)Ba$_2$Cu$_3$O$_{7-\delta}$, YBa$_2$Cu$_4$O$_8$ andBi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. The mean-field transition temperature,$T_c^{mf}$, in the absence of fluctuations lies well above $T_c$ especially atlow doping where it reaches as high as 150K. We show that phase and amplitudefluctuations set in simultaneously and $T_c^{mf}$ scales with the gap,$\Delta_0$, such that $2\Delta_0/k_BT_c^{mf}$ is comparable to the BCSweak-coupling value, 4.3, for d-wave superconductivity. We also show that$T_c^{mf}$ is unrelated to the pseudogap temperature, $T^*$.

Fluctuations and $T_c$ reduction in cuprate superconductors