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RAW? No.
[an incorporeal creature] can be harmed only by other incorporeal creatures, magic weapons or creatures that strike as magic weapons, and spells, spell-like abilities, or supernatural abilities.Natural fire is none of those things, so a ghost can pass through a burning building merrily. Nor is a fire elemental any of those thing. Elementals don't have a rule that makes their attacks "strike as magic weapons". Getting hit by an elemental isn't magic damage. Burn is an extraordinary ability (i.e. non-magical), so the special rule doesn't apply either.
Maybe the rule should be different, and it is a simple house rule if you prefer magic elementals, but by RAW the answer is no.
What about a Pyrokineticist using the Burning Infusion? Their kinetic blast is a Spell-Like Ability, would this cause the incorporeal creature to catch on fire?