on a similar subject, CAP 371 has just changed with regards to the use of hire cars. It now stated that if a hire car is to be used to positon crew, then this must be classed as a sector and count towards the flight duty period. It also states that driving a hire car must be limited to 2.5 hours during any duty period.
So if driving a hire car for longer than 2.5 hours during a FDP causes fatigue, then I am sure that 3 hours driving before a FDP causes fatigue also.