We present heat capacity, electrical and thermal transport measurements of kagome metals \(A\)V\(_3\)Sb\(_5\) (\(A\) = K, Rb, Cs). In all three compounds, development of short-range charge fluctuations above the charge density wave (CDW) transition temperature \(T_\mathrm{CDW}\) strongly scatters phonons via electron-phonon coupling, leading to glasslike phonon heat transport, i.e., phonon thermal conductivity decreases weakly upon cooling. Once the long-range charge order sets in below \(T_\mathrm{CDW}\), short-range charge fluctuations are quenched, and the typical Umklapp scattering dominated phonon heat transport is recovered. The charge-fluctuations-induced glasslike phonon thermal conductivity implies sizable electron-phonon coupling in \(A\)V\(_3\)Sb\(_5\).