Filamentation is a type of magnetohydrodynamic instability that may develop in a current-carrying plasma. It is supposed that filaments, individual current channels, are formed due to thermal instabilities. The growth of these instabilities is determined by the behavior of the electrical conductivity of the material depending on its thermodynamic parameters. If the conductivity increases with temperature, as is the case in a plasma, thermal instabilities should give rise to the formation of separate current channels. This paper presents an analysis of the development of thermal instabilities in imploding plasma liners performed in terms of small perturbation theory. The theoretical predictions are compared with the results of experiments conducted on the IMRI-5 facility at a current of amplitude up to 450 kA and rise time about 500 ns.