The Brownian-type molecular dynamics simulation is revisited and applied to study the thermal and geometric properties of four mono- and two polyvalent metallic clusters. For the thermal property, we report the specific heat at constant volume C-v and study the solid-liquid-like transition by scrutinizing its characteristic. For the geometric property, we calculate the root mean square relative bond-length fluctuation delta as a function of increasing temperature. The thermal change in delta reflects. the movement of atoms and hence is a relevant. parameter in understanding the phase transition in clusters. The simulated results for the C-V of alkali and aluminum clusters whose ground state structures exhibit icosahedral symmetry generally show one phase transition. In contrast, the tetravalent lead is quite often seen to exhibit two phase transitions, a premelting process followed by a progressive melting. In connection with the premelting scenario, it is found here that those (magic number) clusters identified to be of lesser stability (among other stable ones) according to the second energy difference are clusters showing a greater possibility of undergoing premelting process. This energy criterion applies to aluminum clusters n(Al) = 28 and 38. To delve further into the thermal behavior of clusters, we have analyzed also the thermal variation of delta(T) and attempted to correlate it with C-v(T). It turns out that the premelting (if exist) and melting temperatures of the smaller size clusters (n less than or similar to 50) extracted from C-v do not always agree quantitatively with that deduced from delta. (C) 2004 American Institute of Physics.