In 1997, a Rayleigh-Bénard experiment evidenced a significant increase of the heat transport efficiency for Rayleigh numbers larger than $Ra \sim 10^{12}$ and interpreted this observation as the signature of the Kraichnan's ''Ultime Regime'' of convection. According to Kraichnan's 1962 prediction, the flow boundary layers above the cold and hot plates -in which most of the fluid temperature drop is localized- become unstable for large enough $Ra$ and this instability boosts the heat transport compared to the other turbulent regimes. Using the same convection cell as in the 1997 experiment, we show that the reported heat transport increase is accompanied with enhanced temperature fluctuations of the bottom plate, which was heated at constant power levels. Indeed, for $Ra < 10^{12}$, the bottom plate fluctuations can simply be accounted from those in the bulk of the flow. In particular, they share the same spectral density at low frequencies, as if the bottom plate was following the slow temperature fluctuations of the bulk, modulo a constant temperature drop across the bottom boundary layer. Conversely, to account for the plate's temperature fluctuations at higher $Ra$, we no-longuer can ignore the fluctuations of the temperature drop across the boundary layer. The negative skewness of fluctuations at high $Ra$ supports the picture of a boundary layer instability. These observations provide new evidence that the transition reported in 1997 corresponds to the triggering of the Ultimate Regime of convection.