  Employing numerical simulations, we provide an accurate insight into the of
heat transfer mechanisms in the Rayleigh-B\'enard convection of concentrated
emulsions with finite-size droplets. We focus on the unsteady dynamics
characterizing the thermal convection of these complex fluids close to the
transition from conductive to convective states, where the heat transfer
phenomenon, expressed in terms of the Nusselt number Nu, is characterized by
pronounced fluctuations triggered by collective droplets motion [Pelusi et al.,
Soft Matter 17(13), 3709 - 3721 (2021)]. By systematically increasing the
droplet concentration, we show how these fluctuations emerge along with the
segregation of "extreme events" in the boundary layers, causing intermittent
bursts in the heat flux fluctuations. Furthermore, we quantify the extension
$S$ and the duration $\mathcal{T}$ of the coherent droplet motion accompanying
these extreme events via a suitable statistical analysis involving the droplets
displacements. We show how the increase in droplet concentration results in a
power-law behaviour of the probability distribution function of $S$ and
$\mathcal{T}$ and how this outcome is robust at changing the analysis protocol.
Our work offers a comprehensive picture, linking macroscopic heat transfer
fluctuations with the statistics of droplets at the mesoscale.
