That is one long, boring ride. On the other hand it might not be as boring on a bike, being out in the elements, experiencing the landscape a bit more. With the right equipment it won't be too bad. Can you borrow someone's touring suit?
I was just checking around and found this thread. I used to live in S Cal and now I live in Phoenix.
It has been in the low 30s at night and in the mid 50s in the day (below normal temps) here in Phoenix. So it is cold. The AZ/CA border is about 165 miles. From Quatzite it is about 150 or so. I have done this ride on a Gold Wing but not on my Monster. Be prepared for cages doing 90+ mph. Once you get near Phoenix on the west side on I-10 traffic gets heavy and often comes to a near stop. If you are going to the east side of Phoenix you will have heavy traffic on I-10 from west to east (about 1 hours ride).
I would not feel comfortable riding it at night and, if I were you, I would ride it in the daytime. There are a couple of rest stops you can stop at to rest up in AZ, one near the border and one near Phoenix.
It is a boring long ride in the cage so I think it would be just as boring on the Monster.
If you do it, be safe and watch your six for those crazy cagers.