Assuming he's in shed (most snakes when in shed do stay on the cool side, btw) I'd wait a day or so after he sheds to offer him a meal. He should be acting a bit hungry then- I sure hope so.
Your BP is unusual for BPs to be active at feeding time, & not hiding. But that's okay- snakes have their own quirks & you know your snake personally, we don't- so follow your experience when offering him food.
Many snakes do learn NOT to strike when always being fed pre-killed, so I wouldn't worry about that. That's why we never want to suddenly feed live to a snake that's accustomed to eating p/k rodents, as they're likely to get hurt* because they won't expect the rodent to fight back. (*unless it's a live but helpless rodent- ie. a mouse or rat pup with eyes still closed will not fight back)