Engine fan and hot exhaust

[Tradewind25]

Hi

I have a 12 plate Tdi with 1800 miles on the clock. A couple of times recently I have returned from a drive of around 15 miles to discover the following when switching off:
a) Engine coolant fan runs for several minutes
b) Exhaust tailpipe smells very hot - the bumper immediately above it is also very warm.
Coolant and oil temps seem OK (90 and 97 degrees respectively).
When I open the bonnet everything seems reasonably cool; no similar smell of hotness.

Any ideas about the cause?
Anyone experienced similar?

Geoff