Vz commodore won't start on hot days

[Hannahvz]

Hi, wondering if anyone can point me in the right direction. I've got a 2006 vz commodore wagon. The car runs fine almost all the time except for on hot days (32+ in the afternoon) after the car has been sitting in the sun. I'm having trouble starting it. It will crank over and over until it eventually starts (usually after I have put my foot on the accelerator to get it to start up), once the car has started if you don't keep the revs up in the first few minutes the rpms will drop and the car will stall. We replaced the fuel pump after realising it was only engaging some of the time and the car ran fine that night and the next morning. Then that afternoon when it was in the sun again on a 39° day it went back to not starting again. We eventually got it started and black smoke came out the exhaust. The thing we are all confused about is why it is only happening when it is hot outside :/

 

[Fu Manchu]

I'd be looking to replace the crank position sensor located down behind the drivers side exhaust manifold.
It's a fairly typical description of a faulty crank sensor on most makes of car.

 

[Fu Manchu]

Here, this might help. Just found it looking for something else.