A numerical thermal model and the results of stability analysis of a multifilamentary superconducting wire are presented. The model takes into account the temperature dependencies of the conductor thermal conductivity and heat capacity as well as transient heat transfer to the coolant. The one-dimensional heat conduction equation adopted in the model is solved by means of the Crank-Nicolson method. As a measure of conductor stability the minimum quench energy (MQE) is taken. A strong dependence of MQE on current, copper to superconductor ratio and the magnitude of the conductor cooled surface is observed. The influence of duration and spatial length of the thermal energy pulse on MQE is also noticed. The calculations show that an increase of the heat transfer coefficient in the transient nucleate boiling region is not followed by an adequate rise in the critical energy of the conductor.