@MangaAddict69 You're right that wood will burn, but you overestimate how quickly the fire can burn through the wood. For instance, it would take around 20 minutes for a house fire to burn through a hard wooden door. That's a long time.
Considering that this is magical super fire vs magical super wood mecha nonsense, I'd say that even if it does get set on fire it won't be a problem until after the fight's over. Until then his wood robot gets +ATK bonuses from being a walking inferno.