I mmade a bvad approximation that a valve would be open for about 180m degrees.
The longer the open period, the less time spent on the seat to rid the heat collected, which makes life very difficult for the Exhaust. The Inlet, on a naturally aspirated engine does pass ambient air (If it has not acquired too much heat during passage into the cylinder through the induction tract.
On a turbocharged and intercooled engine, the charge is probably at 150'C by the time that it reaches the valve!
But this is relatively cool compared to exhaust temperatures of 650'C and upwards under full load rated speed conditions.. And these are for commercial engines, not tuned for racing or rallying, where specific outputs can be doubled, although at the expense of life probably.
(Ferrari's ideal racing would, he said, disintegrate as it passed the chequered flag! ).
And all valves expose a large area, to collect the head, to heat during combustion, so cooling is importance.
And who knows what shape the valve seat takes under F L R S conditions!
Howard