[Tuidjy]

Devils and arch-devils do not care - they are fire creatures, I guess.
Ice devils suffer from a variety of penalties on armour, attack, defense, etc.
Undead do not seem to mind, at least none of the ones I have as Abysia do.
Normal units get tired more easily - they lose two additional fatigue per turn.
I am not sure whether they do so every turn, or only on turns they do something
that actually increases fatigue, like attacking or spellcasting.

Something I have noticed, although I am unsure whether it is a bug or a feature
is that even when a commander makes himself fire/cold immune, he still gets the
temperature related fatigue effects.