With reference to Agincourt , IIRC it was fought after a prolonged period of rainy weather . In this case French knights when unhorsed would have had a horrible time regaining their footing due to the suction of the mud on their plate armor and many may well have suffocated in the mud along with a number of their similarly armored English foe .
The English archers unencumbered were able to fight much more effectively in muddy conditions and once a knight was down he was easy pickings .
I guess that not only heat could have been an enemy of the fully armored man .
I suspect the Duke of York drowned in the mud .
I do not think that any honor is taken from a man in the way he died on the field of battle , unless he was killed running away . York was there facing incredible odds along with the rest of the English and was most likely covered with the enemies of his king .
As you say ; showing up for the fray is what really counts .