Pasty butt is supposedly caused or made worse by stress, like shipping stress. I'd think temperature swings or anything else that might cause stress could be a factor. I don't know that grit helps it but I think it does. Mine did not have any problem with pasty butt after I started feeding them grit so it will part of the routine for the group in the bator now.
I took some construction sand from a pile I had and put it in a small yogurt cup wired to the side of the brooder. I filled that 6 ounce cup once or twice a day for 28 chicks, but they spilled a lot. Watching them, it seemed like the same chicks just stood there and ate the grit, but none seemed any worse for wear. I think they all got some, just some more than others.
I did not clean every tush that got a little dirty, just the ones where the build-up had started and looked like it might get serious. If the vent was plugged, I was careful to soak so I would not injure the chick when ripping the dried poo off, but if it was just in a small amount of fluff, I sometimes just pulled it off. If the fluff is gone, there is nothing for the poop to stick to. I'm not sure if it starts in the fluff and backs up or it just plugs the vent, whether there is fluff for not. I suspect it could be either.