The emission of nuclear clusters is investigated within the framework of the isospin-dependent lattice gas model and the classical molecular dynamics model. It is found that the emission of an individual cluster which is heavier than proton is almost Poissonian except near the transition temperature at which the system is leaving the liquid-vapour phase coexistence and thermal scaling is observed by the linear Arrhenius plots which are made from the average multiplicity of each cluster versus the inverse of temperature in the liquid-vapour phase coexistence. The slopes of the Arrhenius plots, i.e. the 'emission barriers', are extracted as a function of the mass or charge number and fitted by the formula embodied with the contributions of the surface energy and Coulomb interaction. Good agreements are obtained in comparison with the data for low-energy conditional barriers. In addition, the possible influences of the source size, Coulomb interaction and 'freeze-out' density and related physical implications are discussed.