Are you previewing them while equipped with a weapon that has a fire damage enchantment?
Enchantments are usually responsible for the visual effects when drawing, switching, and previewing weapons. I saw sparks or a red aura on the Oaken Order previews, depending on which bar I was on.
Nope no fire. Nirn, charged, precise and powered across the characters I've tried them on. The flames disappear after a few seconds in preview.
Those are traits, not enchantments. It sounds like you're describing the normal enchantment effect that's added to all weapons that have enchantments but without special particle effects (like the ones crown store monster arms weapons have).