One‐dimensional steady‐state radial profiles of a classical Z pinch are calculated. The effects of ion thermal conduction and bremsstrahlung radiation losses are included self‐consistently, as are Ohmic heating, pressure balance, and an equation of state. It is shown that the upper current limit of approximately 1.4 MA for an equilibrium pinch found when only bremsstrahlung losses are allowed is virtually unaffected by the inclusion of ion thermal conduction. However, solutions with lower currents are now allowed. The profile‐smoothing effect of ion thermal conduction is not sufficient to produce a pressure profile stable tom=0 modes. Total losses due to radial conduction are shown to be small for a thermonuclear plasma.