Is this the slave soleniod on the engine or the starter solenoid thatís on the starter? Canít say I ever heard of one smoking. Once started the soleniod should open so no current should be flowing through it. Could the noise have been the starter staying engaged? If so you need to verify the ignition switch is not shorted else the soleniod may have gotten stuck in the closed position.
1997 2400 SCR
5.7 Vortec / Bravo 2