A majority of people with 3D printers have the heated print bed which is quite useful not only for printing but also for acetone smoothing. The bed has a temperature control built in. You place a small amount of the acetone into the container (about a teaspoon or so) without the basket in it and put the jar onto the printer bed. Place the item you wish to smooth into the container via the basket and put the lid on. Heat the bed up to around 90-100C (I use 90) and let sit for some time (depends on how large the item is, how smooth you want it, etc). I've been sticking with a 10-15 minute smoothing process with most of my projects.
You can then either remove the lid and take the item out (and put another one in if you're doing multiples) once it's to the smoothness you want or you can let the container cool down and let the vapors become liquid again before opening the jar (they'll condensate on the sides as it cools). If you choose to do the latter, I suggest that once you see the item is almost to the smoothness you want, you tell the printer to cool the bed down since the vapors will take some time to settle back down (and will continue to smooth your item in the process).
I prefer to let it cool since acetone is highly flammable and toxic to your health... I do have my exhaust fan going just in case either way.