I had my first major mishap with my Phantom 3 Standard today.

I have the official DJI Phantom Backpack Carrier, so that I can bring my drone with me on bike rides and find awesome places to fly.  Somehow, and I still can't believe I did this--so stupid!--I must have somehow packed it back away with it still turned on!! (That's the only thing I can think of--if it had somehow turned back on in the backpack, I'd have heard that super loud jingle that plays.)

After 30 minutes riding back in the hot sun, I unpacked my drone to discover in horror that it was turned on in there!  The thing was HOT.  Very hot.  The plastic felt hot, and the metal camera part was actually hot enough that I couldn't touch it without burning my finger.  I turned it off right away and pulled the battery out.  It does not look like the battery split or burst.  There is no fluid or gunk that I can see inside the battery chamber.  I closely inspected the battery, and it looks intact, and does not look bloated or warped.

What should I do other than waiting for it to cool down completely?

I am bracing for the worst.  I am really woried that I fried the sensitive camera components of the Phantom 3.  I mean that thing felt like it came out of an oven.  I'm very uneasy about every packing it up in that backpack again.  I THOUGHT I had turned it off, but I must have forgotten somehow.  Maybe from now I should store it with the battery outside of the unit?  Is that how you guys do it?

Definitely ALWAYS keep the battery out when you aren't flying. Events like this are reminders to do so. All you can do is let everything cool down an check it out. Even when you do firmware updates you have the AC in an open space with a fan of some sort, whether it's a cooling pad or a regular fan, moving air across the AC. Just to be on the safe side you could go through the calibration process, IMU, compass, gimbal, to make sure everything passes the test and then fly in a controlled environment to check. Hopefully it all goes as planned. Good luck and let us know the results.

You got lucky the battery did not explode!  

I always take the battery out after flying. I always check the light if I keep the battery in the drone. Maybe from now on don't leave it in the drone until you get use to not only checking but double checking the battery is off.

Once the battery is completely cooled off, plug it in turn everything on and check in the app if there is any damage to the cell or the gimbal.

Let us know.

It appears not to be damaged.  The Gimbal still freely moves, and there are no alerts or warnings when I sync the app up.  I even took it for a (very) short flight around my backyard.  Everything appears to be in order.  I will let this post as a warning to others to not repeat my mistake.  From now on I will always keep the battery out of the drone when not flying it!

Good to hear it's still flying! Lesson learned

Thanks for posting i Will now always remove the battery when not flying just in case. Good flying to you.

I had a similar  mishap.
Had my remote turned on in the bag for about 1.5 hour.
Burning hot after i took it out. Hopefully it is OK.
I was also burning hot after 1 hour under the Thai sun...close to 40 degrees.