Transporting from home to work (~10 min by car), should I just make my MacBook Pro sleep, or shut it completely down first?
It's perfectly OK to transport it while it's sleeping - I do this all the time.
The disk is stopped and the only power draw is what is required to keep the memory contents (and the fading in/out of the power light).  Any heat it generates during sleep is pretty much undetectable (in human terms).  As long as nothing is connected to it, it shouldn't wake up in the bag.