PVC Drains next to Gas Exhaust Vent Pipe?

[Rhadley]

I am remodeling by bathroom and think it best to replace the old cast iron drain pipe that the shower uses, and the lead pipe that the toilet uses. Both are touching the water heater gas vent pipe. If I replace them with PVC, it seems I would have a melting PVC issue. What should I do with the old drains? They don't leak now, but they are old. See pics

Thanks,