How long does it take for a cell phone's LCD screen to thaw if it's been out in the cold weather?

I have a Katana LX. I came home from college and was taking stuff out of my car and I guess my phone fell out on the ground. I noticed it was missing two hours later. When I went outside (in 32 degree weather), I found it on the ground. I can make and receive calls but the display is just white. My front screen doesn't even come on. I was reading online that it just need to thaw out and it will turn back on. Can anyone tell me how long it will take? This just happen 30 minutes ago. Should I check on it in the morning?