Ok, so not sure if I can edit my original post... it doesn't look like it... so I'm going to "reply" to my own post with an update.
A couple of things to point out; 1. The unexpected shutdown issue DOES in fact seem to be related to heat and improper fan control by the OS (at least in our case). We have had the fan running at high speed for two days now without any unexpected shutdowns. Prior to manually running the fan speed up, the laptop would get hot (we suspect) and shutdown several times per day. 2. We found a better fan control program with much more capability. "Macs Fan Control" available here: http://www.crystalidea.com/macs-fan-control. Awesome little program! You can view ALL temp sensors in your computer and set the fans manually, to be controlled by the OS automatically, or to ramp up based on a low/high temperature. Very handy program indeed. Totally free and much more feature packed than the simple SMC Fan Control program.
So in summary, at least in our case, the unexpected shutdowns (due to Mavericks) have been solved by running the MacBook Air's fan at higher speed. Hopefully Apple will fix whatever is causing the fans to not be controlled properly. If you find that running your fan(s) faster fixes your problem, please post a reply here so others will know... or at least click the "Like" link at the bottom right of this post, so others can see it is a "Like(d)" solution. Hope this helps. If it doesn't fix your problem, also please post that info.