This paper presents simulation results on the dynamics of 2D arrays of ultrasmall normal tunnel junctions at finite temperature, focusing on the possible Kosterlitz-Thouless-Berezinskii transition of charge unbinding. In the case of an array with zero self-capacitance, we find a reasonable agreement between simulation results and the theory. We perform finite-size scaling analysis for linear and non-linear conductances. We also study the effects of self-capacitance and random fractional offset charges, which may be relevant to the experimental situation. In both cases, linear conductances show activated behaviour. A random charge distribution with relatively strong disorder could explain the experimental values of the activation barrier energies.