We present a molecular dynamics (MD) study on the structure of self-assembled monolayers (SAMs) of alkylthiolates on various metal surfaces, with especial attention to Au(111) and Ag(111). Variations in the structure of these SAMs as a function of temperature and alkyl-chain length are systematically investigated. The MD simulations are performed by using a recently developed force field based on second-order Moller-Plesset perturbation theory calculations. Good agreement between the present results and the existing experimental data is found on Au(111). On Ag(111) the comparison between theory and experiment is also satisfactory for alkylthiolates with no more than 14 carbon atoms. The dependences of the average tilt angle of SAMs on temperature and chain length are easily understood by means of a simple single-chain model.