MarkT:
The RFP12N10L MOSFET is not suitable, it has a very high on-resistance.
Hm OK, thanks for the advice.
I found two MOSFET that seem suitable, first the FDP6030BL with 30V, 40A and 18mOhm. It also has a Ptot of 60W so no heat sink required I assume?
Another one I found is the IRF3710.
This one has 100V and 35A, and also an RDS of 18mOhm?
I think the first one suits better, but what do I now 
Again, thanks a lot, every help is appreciated!
PS: Of course I already use a free-wheel diode, some things still stuck from my electronics course a few years ago