Many good suggestions have been offered already, 
but here's a few of my suggestions:

* Pack and transport cels yourself (never dealt 
with any moving companies, but if I did I 
wouldn't let them near my cels)
* Pack cels last
* Unload cels first (and make sure they go into a 
safe place that won't see much traffic until 
you're done moving in -- one suggestion would be 
to keep them at a trusted friend's house if you 
know anyone near where you're moving to)

The rest of these are dependant on weather (and 
assuming you're traveling by car), although it 
never hurts:
* Keep the air conditioning on (I usually move in 
summer & my latest move was to a co-op in 
Florida, so this can be an issue at times)
* Put celbooks on top of everything else, but 
place something light on top to reduce heat from 
sunlight (sheet of cardboard, etc.)
* If your road trip is going to be more than 1 
day, make sure to bring your celbooks into the 
hotel/wherever you're staying (better controlled 
climate and less chance of theft)

What I've listed here is mostly just what I've 
personally done as precautions.  Hopefully you'll 
find some of these ideas helpful!