I have a Thumler's Tumbler. They are made to run for weeks at a time polishing rocks. Make sure the motor has been lubed about every month's worth of running (there is a place at both ends to run some in). The motor gets warm; almost hot, that is normal. Put some walnut shell media, treated with polishing compound, in it and let it run until cleaned to a dull finish. Then run the cases in some corn cob media to give them a real polish. I have a Lyman's turbo 2500 for corn cob media.
BTW I regularly run both tumblers while I am away at work, up to 12 hours at a time.
Make sure the vibratory types are on a smooth surface and do not over load them. I put mine on a concrete floor, then it gets good air circulation to keep it cooler and I do not have to worry about it "walking" off a table. It is noisy, so I do not run it over night as the reloading room is in the basement under our bedroom. The Thumler's Tumbler can be run over night with only a low noise being made, not enough to disturb sleep. I put it on an old piece of carpet to help absorb some noise. Do not put the vibratory type on carpet as it will restrict the cooling air flow. As has been said; polishing, it is only for looks, as long as the case is clean (free of grit and corrosion); it will be fine. Good Luck and Good Shooting