How exactly are you thawing these rats "during the day"? Improper thawing causes spoilage & since BPs do not eat "carrion", the smell of spoiled rodent meat will turn them off eating. And if you've thawed improperly*, warming them up afterwards just accelerates that process (rotting!)- & that could be why your snake wants to gag when presented with these rodents.
*Food safety is much the same whether it's your snake's food or your Thanksgiving turkey: Either thaw in the refrigerator (this is very slow, since air-transfer of temperatures is very slow & rats have thick insulating fur which makes them take quite a while to thaw in the middle) or thaw in COLD water (faster, & depends on how big the rat is- can take a couple hours with water changes until completely soft all the way thru- feel by hand to make sure though).
When thawing in cold water, some like to thaw in a plastic baggie- to avoid washing off too much scent, but you can also use your tongs to pinch-damage the rat's nose to release more scent.
If you thaw in a baggy, just understand that is slower than thawing directly IN the water (because there's a little air in the bag with the rat) .
DO NOT thaw rodents by leaving them sit out on the counter top- as previously mentioned, thawing in air is very slow, which means the outer parts of the animals are spoiling before the inside is yet thawed. Snakes can SMELL that spoilage.
DO NOT thaw rodents in hot water, for the same reason- only put completely-thawed rodents in warm water briefly to warm them up for snakes right before feeding- and for best results- you might also use a blow dryer (especially to heat up the head, where you want the snake to target) & offer quickly, since they cool off fast.
And IF you're thawing the right way, it might just be that your snake PREFERS the taste & aroma of mice over rats- some do. And do bear in mind that neither domestic rats OR domestic mice are their natural diet in the wild.![]()