Check your hearth, but it'll be tight!
Provided that the hearth is rated for zero clearance to combustibles in back, UL 127 (the standard for manufactured fireplaces) limits the temperature rise on surfaces intended to be in contact with building material to 90°F above ambient. Considering that building wiring materials are rated to 194°F and you need to have some margin for wire heating and the minimums of derating (we can't derate below 15A here assuming a general purpose branch circuit on a 15A breaker), you're limited to a wire temperature of 167°F maximum or an ambient temperature of 77°F.
NM cable can survive 90°C exposure, but needs to be protected from physical damage, and conduit's too chubby for the job. However, you can use 12/2 NM (due to the need to derate the ampacity of the cable -- a 12AWG/90°C wire can handle 30A, but we are derating it to 15A instead) in a suitable surface raceway (less than 1/2" deep, and rated for exposure to 90°C) to make this run.
Tip: install the raceway behind the hearth first -- you'll have to sort of slide it into place, and you'll need to be judicious about where mounting clips/brackets go, as well.