You don't have to leave them 24hrs or more. I just make sure mine are at least room temp and if I put them in the bator quickly then I leave the turner unplugged for a day or so. I think that's actually better than getting warm eggs in summer, letting them cool, and then heating them back up again. Seems rather pointless. Plus all they do in the bator is sit there anyway aside from when you turn them or if you have the auto turner going and it does no harm to miss turning for 1 day so what difference does it make leaving them sit outside the bator.... You also don't have to set them the day you get them but the longer they sit the lower the hatch rate. Most suggest setting within 7 days of being laid and no more than 10 for best hatch rate.
How quickly you can use a bator after cleaning depends what you used to clean it. Bleach can take awhile to evaporate out. If you wipe with vinegar it helps neutralize the bleach and will evaporate quicker than bleach. To truly kill everything it's suggested to soak in a bleach mixture, leave to dry in sunlight (some things can only be killed by time and sunlight and not even by bleach), wipe with vinegar, rinse well, and let dry before using. Between hatches I've just wiped with vinegar and been fine but I try to soak the bators at least once a year to kill everything.
