But then cooling the phone/rice reduces the amount of evaporation, so you might just as well leave it out on the kitchen counter. You need to put it in a sealed container anyway so it doesn’t absorb moisture from the room.
A few years ago I was photographing an event in the rain and all the buttons on my second camera stopped working because it got too wet after sitting on my hip all day. Fortunately the shutter and power button still worked, but nothing else. Anyway, when I got home I just set up a small fan heater blowing on it all night on low power. By the next morning it was pleasantly warm and ready to go.
If you do a Google search, you can find a couple of companies that make machines designed to dry smartphones, perhaps using a vacuum. You’re probably not going to run out and buy one of those machines when you drop your phone in the sink but some of those storefronts that offer smartphone repair may have one. So if you’re willing to pay the fee, you might look into taking the phone to them.
What I’ve read is that you want to get as much of the water out as possible by mechanical means rather than evaporation. Shake it, use compressed air, vacuum, whatever to get water out. Evaporation is the worst method, because whatever was dissolved in the water will remain behind and cause problems. That seems to be exactly what happened to my phone that went in the pool.