Well I warm up my F/T by taking the ziploc bag they're sitting in and putting it in hot water to thaw out and then I just warm the head with the heat lamp.
There's no definite yes or no on whether or not your snake will then only take live if you feed it live. I've never had a problem switching between one or the other but my cinny will eat anything you put in front of him, live or f/t. I'd probably find the best eater in the bunch and let it eat the live rat if you really can't kill it yourself. I would never try switching to mice unless it was my last resort. And clearly your boy is a breeding size male so I'd never be that desperate unless he lost a lot of weight and refused a live rat first.