I had the same problem mid summer last year, and it turned out to be the relay which afterwards I found out was a common problem according to my dealer.
haha right now my 98 boxster is having the EXACT same problem
its at the dealer right now, should be getting it back tomo then i iwll tell you wat the problem is
yup it was some sort of relay..but its not a simple one
it was under warranty so i don't know about the price but the charged 600 and something AUS dollars plus 150 in labour..