Question: I bought my base model 15" MacBook Pro w/ Touch Bar the day it was released, and I just received it yesterday. I've been copying and downloading all the data and files that I needed and the battery didn't last me more than 5 hours, if even 4. I have no idea what is wrong with it, but it's really overheating and I almost never hear the fan running, which also alerts me.

Today I played Crossfire, a game with very basic graphics, on Windows 10 Bootcamp and it was ON FIRE! I had to close the game because of the laptop's temperature. Again, I did not hear the fan.

Things I've done:

* Reset the System Management Controller (SMC)
* Run hardware diagnostics by restarting and pressing the `D` key while booting. This was the first time I actually clearly heard the fan. The overall results were that it found no hardware problems.
* I called Apple, but they had no idea what they were telling me as they were following a written script, although a Senior Advisor was talking to me regarding the issue.

Now I have had it just for two days so far, and I have a two-week return period. Should I wait more and see how everything will work out, or should I return it?

Has anyone experienced the same issue? Is there anything else for me to try?

Answer: 
The problem you discribed is exactly the same that I have with my new MBP 15" Touchbar (2,9Ghz, Radeon 460). 
The reason why it's overheating is, that the fans do not automatically accelerate when there's a higher workload. They are continuously running at 2000 rpm. 

My solution: Use iStat Menus

There you can manually increase the rpm to medium (3500-4000rpm) and high (4500+).
You will see, if you manually adjust the fans, the MBP will work great and there won't be any overheating issues.

BUT that's not how a notebook should work. It must automatically adjust the fans.
I talked to several apple support guys (In Germany) and they all told me, that they havent experienced such a thing yet. I did the same things like you, resetting NVRAM, resetting SMC and I even reinstalled the OS. Nothing helped.

It may be a firmware issue that will be fixed in the future. However it seems like just a minority of MBP Touchbar customers are facing this issue.
Most likely I will exchange my notebook in January (since it's not available at the moment xD )
I am having the exact same issue, & even after apple provided a replacement device to me today at 6pm this issue has not been resolved. 

Backstory: My original device was picked up 2 weeks ago, from the Pasadena store. Immediately that night I noticed that the heat was so bad the equipment was hot to touch, and even spreading to the sides and top other portions of the device. I reported it via online chat and immediately apple business contacted me the next day scheduling a Genius Bar appointment. During that appointment the genius tech wouldn't tell me what was wrong but stated after only a couple minutes that the device needed to be sent to engineering once it was returned for investigation, and they would provide a replacement no questions asked. The replacement device arrived tonight and 30 minutes into using it (Safari, Sublime text install, and web browsing on a solid surface it was so hot that it begin causing other issues( slowed keyboard response onscreen, screen flicker, lag). I contacted support again, and they immediately setup an appointment with Genius Bar for 6am tomorrow. I am really losing faith in this model but don't know what to do at this point because it appears that no one knows what the root cause of the issue is. Friends of mine have the same model without issues. If anyone has any details please share.