Can I keep wet cloth behind my iPhone 12 while charging?

I would not advise having any kind of wet near the iPhone when charging. The iPhone should not have that much heat when charging. And, the iPhone uses the case to dissipate heat when charging, so it should be left so air can get around it to help lessen the heat. I would not lay it on anything cloth or otherwise. You can leave it on a table, or a wireless charging pad, etc.

If water damage occurs, you would be responsible, voiding the warranty coverage.

If you want a tip: power-off your iPhone during the charge and it will charge faster because the battery won’t be running.

▷ Apple Battery Guide. 

Water and electronics tend not to coexist at all well with corrosion and shorting, and adding evaporative cooling would not be something I’d suggest doing. That because of the risks of corrosion, condensation, deposition, and shorting.

Warming is normal during charging.

If you suspect your iPhone 12 is overheating while charging, get it checked by Apple or an Apple authorized service provider.

All of my chargers get hot during use. 😉

Trust me, that cloth will do more harm then good. Unless the phone is so hot it hurts, it's fine.