91 Lexus LS 400 overheated, now won't start

91 Lexus LS 400, V6, 130,00 miles. The temperature gage had been at a higher level than usual for about 3 weeks, but not in the red zone. Coolant and oil levels were fine. On the day the car died, I was driving at about 35mph, noticed steam coming from under hood, smelled burning coolant, saw the temperature gage shoot all the way to the top, so I went to pull over, and the engine cut off on its own. Checked fluid levels after it cooled off and I still had coolant and oil, and the coolant was not mixed with oil. Car would crank, but not start. Had it towed home. Kept trying to start for several weeks, now the battery is dead. Any ideas on what the problem is and how costly it would be to repair? Thanks!