The FCC proton beams pose a severe challenge for the robustness of the beam dump and protection devices. Depending on the local beta-function, already a single 50 TeV bunch can induce damage in typical absorber materials presently used at the LHC (e.g. Graphite or carbon composites). In order to safely absorb the FCC beams in a LHC-like dump, the beams need to be sufficiently diluted across the dump upstream face. This study assesses the dilution kicker requirements and derives energy densities, temperatures and stresses in the dump core and windows for regular sweeps and dilution failures. In particular, the effect of overlapping shower tails from neighbouring bunches and neighbouring branches in the sweep pattern is quantified. Based on the obtained results, the implications for the overall dilution system design are discussed.