BMW: B<W 318i 1984 automatic wont start when hot, inhibitor switch, costly affair

Question
Hi Josh
Please can you help?  I have a 1984 318i automatic with 170,000kms on it.  It is regularly serviced and I love it to bits - its a great car with one exception.
In the morning when its cold the car starts no problems and runs well wherever I drive it.  But if I am driving for
a bit and then stop (say to put in petrol or go to the shops) and then come back to start it, it wont start.  The lights come on and the radio starts, the starter makes no sound and nothing happens.  If I leave it for a bit (10 mins to 45 mins) and then try again it will start straight away.  I also notice that if its a warm - hot day 30 degrees C or above this will always happen until the weather has cooled right down.  My mechanic says its a dirty starter relay and has cleaned it but its still happening. A friend looked at it too and says its the inhibitor switch, but it wont start in Park or Neutral either.  I am getting very frustrated and am nervous that if I take it to my mechanic it may turn out to be a lengthy and costly affair.  I didnt spend much when I purchased the car (about $2500.00 AUD) and its been great to me but I dont want to be stuck with a mammoth repair bill.  When it does start it runs really well and I think its a minor problem but I am getting frustrated.
Do you have any ideas?

Thanks  

Answer
Holly,
 Yes I do have a few ideas.  First off, how long has it been since the starter has been replaced (if you know)?  Starters go bad, much like an alternator or battery.

 Some starters suffer from "heat soak".  This is when you are driving, and the car gets up to operating temperature and since the starter is bolted to the side of the engine it gets hot as well.  All this heat can cause the starter to expand and stick in side it's housing.  This will stop the starter from turning until the metal has cooled.  This sounds like the problem since you are having to wait after you drive it.  To check this problem take a hammer and a friend with you on a short drive.  Try to make the starter stick, so drive it like you normally would.  Stop the car and wait, Then go back to start it.  If it sticks, have your friend (hopefully someone who knows a little about cars) take the hammer and GENTLY tap on the side of the starter while you hold the key in the start position.  This has worked 99% of the time for me.  Tapping the starter will loosen it up and it will turn again.
 If this works, take the car to your mechanic and have him replace the starter ONLY.  No matter what he says you need to do, just have him replace the starter.

 Good luck!
 Josh