We calculate volume-independent ratios of cumulants of the net-proton number distribution up to sixth order in a fireball that cools down after the chemical freeze-out. A hadron resonance gas model is used together with the assumption of partial chemical equilibrium, which fixes the number of observed stable hadrons after the chemical freeze-out. It is shown that due to only weak departure from the statistical Boltzmann distribution, also the volume-independent ratios of higher-order cumulants of the net-proton number show only weak dependence on the temperature. This observation supports the possibility to measure non-critical cumulants at chemical freeze-out even after subsequent cooling in the hadronic phase. Cumulants of the net-baryon number behave similarly, while those for the kaon number vary more strongly with the temperature. Our results are relevant for the current fluctuation studies of the RHIC-BES runs.