Same problem here; a great relief to find I'm not alone in the world of HTC Deisre spontaneous reboot problems.
As with lots of other posters, problems occur seemingly randomly, but with a few common factors:
- phone seems unusally hot when it reboots, especially low in the back ("lower back problems"

)
- endless loops of reboots may ensue, with removing the battery as the only resolution
- the battery itself doesn't seem particularly warm, but SD card and SIM are almost scorching to the touch
- reboots occur with various types of intensive and less intensive use, but are almost guaranteed when using an app for any length of time while charging, and certain (within a couple of minutes) when using GPS while charging (which for me is one of the main features of the phone: to be able to use it for car nav, which is not realistic if I can't charge it while driving)
Just got off the phone with the Dutch HTC Service Center, and had a surprising experience. The operator basically called all forum posters a bunch of liars--which was not the surprise, because others have reported the same experience--but then went on to confirm, from the symptoms I described, that overheating is the problem. He even went as far as explaining that the reboot cycle is the phone's attempt to cool down, and that the charging/GPS connection confirms the diagnosis, and admitted (!) that the problem occurs with more than just my own HTC Desire.
Pickup's tomorrow; processing time should be two or three weeks. I'll report back when I have my phone back in my hands.