The proper brass wool from soldering equipment manufacturers may have flux added which helps. Kimwipes additionally can be used and won't thermally shock the tip.
If you do use a sponge use only a little distilled water so it's just moist. Tap water or a dirty sponge can slowly increase the surface oxidization and if you aren't retinning the entire work surface of the tip regularly it may decrease wettability. When this starts to happen it can be prevented getting worse by using the brass wool.
The other problem that arises when you clean a tip (or recently cleaned) is leaving it powered on for extended periods with no solder. This can also oxidize the tip and bake on flux residue. So when not soldering or done for the day clean the tip and generously apply fresh solder directly over the entire tinned working area. To resume soldering clean it.
I use brass wool and the Pace fiber cleaning tool (1100-0232-P1). It's about $20 with two refills costing around $14 (1127-0013-P2). They last a long time and can clean tips very effectively, especially large and odd shaped tips and tweezers.
The video below shows it in use at 3m50s.