940 GLE- wont start on hot days & after 30 minutes journey

1. On hot days when my 940 GLE is parked directly to the sun, it won't
start from ignition regardless whether it has been sitting for a long time
(like ovenight) or not.

2. After it starts (whether through ignition or through jumping connection
on the solenoid /starter) and then I drive it for about 30 or more minutes
and turn it the engine off and then start it with in 20 minutes, then it
will start right away. However, if the car sit for more than twenty (20)
minutes, then it will not start or crank (unless Jumped)for a long time
(about 2 hours plus (+))and worse if it is hot or humid.

If I leave the key on and jump the connections on the solenoid and
starter, it will spin the starter. Then I can start it with the ignition
key.

Starter and battery are not the problem, the've been checked and fuel
pump relay was replaced just recently.

By the way, once it starts, it drive OK without any problem for as long
as it is not tuned off. Everything on the dash board comes on OK. Radio,
stereo, Horn all works OK.

Finally, it should be interesting to know that, check engine light has
never come-on due to this problem leaving me wondering what now!

Any a suggestions on what or where I should concentrate on?