How long (i.e., how many batteries) can this thing go through before overheating?  I just did 2 and the mini frame seemed excessively hot.  N.B., the second battery was for a mini 1 if that matters.

How hot? It does normally get well over 100F.

Don't worry about it.
DJI have demonstrated flying some of their drones for 72 hours straight without problems.
I've flown 8 batteries back to back several times.

It will never overheat unless you don't fly. It's basically aircooled, so no air = no cooling.

I always turn it on, wait for satellites, then fly and as soon as I land i turn it off. It will always be cool that way, but If you leave it on over a table for long periods to transmit photos or videos via WiFi it will heat.

Just turn off the drone and use the SD card instead.

Thanks all, I really appreciate your posts.  As far as the temperature, I would guess it to be a bit over 120 F.  I do have a temperature probe, so I'll use it next time.

However, I must admit I messed up.  I have one of those small ARC strobes mounted in a 3d printed plastic holder I bought from Firehouse.  That unit gets mounted over the exhaust ports.  There's clearance, but there is some blockage.  I never noticed a problem after flying with one battery, but I guess the heat starts to build up with the second.

I will need to rethink my lighting options for something mounted on the arms.  Too bad, that light was great.

Hi, texgeekboy. Thanks for reaching out and posting your inquiry. The DJI Mini 2 will normally heat up when being used but as long as you're flying within the Operating Temperature of 0° to 40°C (32° to 104°F) you should not be experiencing any overheating even with continuous flight.