I agree that as a rule, offering uncooked prey is best. But: one trick that works wonders to get picky colubrid hatchlings feeding is to boil the prey, then cool it down to room temp before offering (and then once they realize a mouse is indeed food they get weaned onto regular thawed prey). The idea is that it alters the scent of the prey enough to get the snake to get over any olfactory hangups that might be at work.
So, what could be going on in this case is less related to temperature than it is to some alteration of the smell of the rat. Surface body temp on a live rodent is about 90F, so the temperature hypothesis isn't obviously true. It could be tested by heating the rat, then cooling it, then offering it. If the snake is always offered prey from the same source (rodent breeder/seller), getting a different smelling rat from some other vendor to see if there's a difference in response can help to troubleshoot the cause of the fussy eating behavior.
Different issue: others can certainly comment more on behavior, but when my (only) BP is 'out cruising', he's not hungry. Mine is hungry when he's in the ambush position. There might be some element of misinterpreting the snakes' readiness to eat at play (though maybe not; snakes are funny critters).