  We study the process of thermal convection in jammed emulsions with a
yield-stress rheology. We find that heat transfer occurs via an intermittent
mechanism, whereby intense short-lived convective "heat bursts" are spaced out
by long-lasting conductive periods. This behaviour is the result of a sequence
of fluidization-rigidity transitions, rooted in a non-trivial interplay between
emulsion yield-stress rheology and plastic activity, which we characterize via
a statistical analysis of the dynamics at the droplet scale. We also show that
droplets' coalescence induced during heat bursts leads to a spatially
heterogeneous phase-inversion of the emulsion which eventually supports a
sustained convective state.
