Dynamics of dense microemulsion droplets forming ordered cellular phases as temperature increases are investigated by neutron spin echo spectroscopy (NSE). The shape fluctuations of droplets are shown using a specific contrast. Their relaxation time tau(f) is obtained by analysis of the NSE curves, which also reveals the short-range Brownian motion (diffusion constant D-0) of the "caged" droplets. The thermal dependence of D-0 and tau(f) supports the notion of entropically driven interdroplet steric repulsion stabilizing the cellular phases.