Any tips for using an open hearth fireplace?
It is correct that the fireplace draws all its input air from the room (tho' some modern fireplaces are designed with separate input feeds thru the brickwork, which means only that they burn just fine with a sealed glass door in front).  If you can find one, get a log support which includes a row of "C" - shaped tubes which take in air, heat the air due to proximity to the flames&amp;logs, and exhaust that air back into the room rather than up the chimney.
Here is one example. Sadly,  not cheap enough (probably) to be worth buying just for your short stay.   grate heater