It may be easier to rent a car, but I can't imagine it being cheaper than an advance purchase rail fare.
It is worth checking
http://www.hertz-transfer.de/ to see if there are any available for your journey, but if not, you're looking at around approaching €300 for a one-way hire in a 5-seater (more if you want automatic transmission). Then let's say 10l/100km, 500km, €1.35/l and that's another €65 on fuel. And maybe €8 for the vignette.
If, however, all the advance purchase rail fares are gone and there is a transfer car available, you could get that down to €170 (vs €266 for a walk-up rail fare).