The paper presents a theoretical study of ion transport in a gas-filled RF quadrupole. The equilibrium energy and space distributions of ions cooled in the transport quadrupole are calculated using the program taking into account effects of elastic ion-molecular collisions. The dependence of these distributions on ion mass and quadrupole parameters is investigated both inside the quadrupole and after ion extraction into vacuum. It is shown that the RF field leads to ion cooling, and the phase volume of the ion beam after extraction exceeds the value predicted from equilibrium ion distribution parameters inside the quadrupole. The approaches to optimization of ion transport from the source to the accelerator  of the orthogonal time-of-flight mass analyzer are considered.