Heat is transferred from the engine block into the coolant which is circulated through the radiator where the heat now in the coolant is dissipated.
The coolant is always cooler than the block or else heat wouldn't be transferred to it.
In fact the block itself on the inside where combustion takes place will be many 100's of degrees C.
So it is a continuous transfer of heat from combustion to the block to the coolant, the block nearer combustion will be a lot hotter than the block next to the coolant chambers.
When you turn the engine off, the coolant circulation stops, therefore the coolant that happens to stop around the block has a lot more heat than normal transferred to it. So therefore It will heat up a lot more after the engine has been turned off.
That's my take on it.
Its a similar reason to why a lot of diesels have "turbo timers", ie it will keep the engine ticking over for a couple of minutes after you "turn it off". It does this in case you've been working the engine hard and it is hot, ticking over will allow the whole engine to cool some - presumably with a bias towards specifically letting the turbo cool.
Edit : Whether the fans should come on after turning the engine off I don't know. In many ways it is pointless because the coolant isn't being circulated through the rad, but it would blow cool air into the engine bay.