It does get hot, specially in the bottom side of the phone. Not always, but when running specific tasks. I noticed the S3 getting hot very fast when playing Adobe Flash videos.

 

Warm when browsing/streaming videos, hot when gaming!

 

Everything I use runs hot. HEYYYOOHHH

 

Sometimes when charging the device in a car it can get hot, but the main time it gets hot is when using data in weak signal areas. The power draw is high, so the device gets hot.

Mainly seems to be when in 3g areas.

 

Of course it does. At this thickness and with this amount of processing power no phone will run cool.

 

39 degrees is nothing to worry about. I think max temp for most batteries is 120F, which is close to 49C. At least that's what it was on my HTC rezound. That thing would heat to 39C with just moderate use. With the S3, the hottest its gotten was 38C and that was after about 40 minutes of playing ME Infiltrator, which is a fairly graphic intensive game. It idles between 25C and 30C depending on the ambient temp. Right now, its sitting at 25C, but it's pretty cool in my office and I haven't used the phone in the past hour.

If you're regularly hitting 39C with light-to-moderate use, that may be a concern. However, if it reaches that temp occasionally and only with heavy use (gaming, streaming video), I wouldn't worry.

 

I think much depends on signal conditions. When in marginal areas, mine can run pretty hot.