Hi, Ray and dbu: Good news, I figured out the "bug" by myself today! It is indeed the key problem:
I drove the van out and, surely it won't start after I stopped for 10 minutes.
I finally noticed that the Immobilizer light was still flashing even after the key was turned to "On" (the position just before ignition). This could only mean the van did NOT recognize the key.
I changed to another spare key, the Immobilizer light was OFF, and yes, the van was started easily.
So it's the key problem --- although I still can't understand why it happens when the engine is warm. I'll go to the service department very soon.