Dynamics of methanol sorption on loose grains of new composite adsorbents “LiCl in mesoporous silica” was studied by a Large Temperature Jump method under typical conditions of adsorption cooling cycle. Effects of number of the adsorbent layers, salt content, grain size and cycle boundary temperatures were studied. The kinetic curves for grains of 0.4-0.5 mm size were shown to obey a simple exponential dependence m ~ exp(-t/τ). For grains of sorbent LiCl(21 wt%)/SiO2, the characteristic time τ for methanol sorption (desorption) increased from 70(32) to 193(111) s when the number of layers enlarged from 1 to 4. The decrease in salt content to 13 wt. % resulted in faster adsorption (τ = 44 s) but smaller variation of the uptake. The initial Specific Cooling Power was estimated to be 7.9 and 2.8 kW/kg for 1 and 4 layers, while that corresponding to 90 % of the equilibrium sorption was reduced to 3.1 and 1.1 kW/kg being still practically attractive. This experimental study of sorption dynamics gives a clear evidence of the possibility to build quite compact cooling devices which utilize loose grains of the LiCl/SiO2 composites.