A diesel car's idle can rise suddenly because it may be regenerating the particulate filter. Active regeneration raises exhaust temperature to oxidize accumulated soot, and many diesels change idle, cooling-fan and start-stop behavior while that happens.
What can appear at the same time
A slightly higher idle, the cooling fan, a hotter exhaust smell and changed start-stop behavior can coincide with active regeneration. The exact indicators are specific to the manufacturer.