I spent two hours tonight trying to get the phone to stop spontaneously rebooting during the boot process--without success. I finally gave up and used the Volume Down and Power buttons to select the FACTORY RESET option; not sure what the difference is between that and the CLEAR STORAGE option. Anyway, the phone spontaneously rebooted again during the account setup process! Next, I used the buttons again and selected the CLEAR STORAGE option. This worked. I've spent the last hour setting up my account and re-installing applications--including AppBrain.
I got a little impatient and installed four or five applications at the same time when -- BOOM! -- the phone started spontaneously rebooting again. (Prior to the FACTORY RESET and CLEAR STORAGE steps I performed above, installing four or five apps at the same time would almost *always* cause a spontaneous reboot--but I figured that was related to the problem that was causing all the other spontaneous reboots. I guess I was wrong. So much for Android's stability.)
Although the phone doesn't seem too warm (thanks, Kratzer), I've removed the battery and am letting the device (and me!) cool down for a while. Suffice to say I am not happy.
UPDATE: After 15 minutes, I inserted the battery. It hasn't spontaneously rebooted yet--but it most likely will...and at the most unexpected and important time. What should I do? Call VZW Tech Support? Take it to my local VZW store? How can I convince them that there is truly a problem with the phone? I suppose I can simply install four or five applications at the same time...but that seems like a poor way to demonstrate that there's a problem with the phone, IMO.