Rapidly draining battery on new X-S10?

First post here. After years with a Canon DSLR I decided to try the Fujifilm system and bought an X-S10 with the 16-80 lens a couple of days ago.  I brought it home and familiarized myself with the menus and settings for about an hour after the battery had charged.  I changed some settings but nothing major.  Yesterday morning I took the camera with me on a quick walk and took about a dozen photos, all jpegs, trying out the film simulations and the aperture and priority modes when I noticed the battery indicator was red and on one bar.

I charged the battery again this morning and went out intending to take a lot more photos, again all jpegs.  When I pressed the review button after taking a handful of photos there was a little square "processing" animation on the LCD and the indicator light started glowing red and orange.  This went on for at least a minute or two before I decided to turn the camera off.  Even though the camera was off the indicator light stayed on (I think orange).  I wasn't sure what to do so I removed the battery and the light went off.

I put the battery back in, took a couple more photos and then had lunch outside (camera in a case in the shade and the temperature was about 60F).  I forgot to turn the camera off but I know it shuts off automatically after a few minutes.  When I grabbed the camera after about 20-30 minutes body was very warm to the touch, the indicator light was red, and the battery was nearly out of juice, and the camera would not let me take a photo (I didn't notice an overheating warning and I don't even know if the X-S10 has one).

After coming home and charging the camera for an hour I went to preview the photos but there were no photos on the card.  Nothing from yesterday and nothing from today. I did not delete them.

Has anyone else had this problem or heard of anyone having this problem?  Is there anything I could have done to cause the battery to drain so fast?  As I said, I didn't make any significant changes to the settings (and didn't turn on any of the more power intensive settings like PRE-AF) so I'm thinking there's something wrong with either the battery or the camera.  Other than take it back are there other things I can try to see what is going wrong?  I reformatted the card and reset the camera back to factory settings.

Any suggestions are appreciated!