Disclaimer:
I can't recommend this since I don't have the electrical schematic and engineering design of the insert,
So purely from a discussion standpoint, and not recommending anyone take any action at all...
If it were mine I'd check to see if the air vents at the bottom were the heat intake or the fire box inlet,
And check to see if the top air vents where warm air discharge.
If this is the case, I might set a row of ultra cheep, low consumption DC computer fans to either push air into the intake, the least efficient way to force air,
Or if the front of the unit stayed cool enough I might see about drawing warm air out of the upper vents.
Since the computer fans routinely come in 12 volts, and low enough consumption they would run for several hours off a 12 volt automotive style battery, with no inverter losses, everything commonly available, I would look into it.
Since this is an urgent or emergency situation depending on outside temps, (Grid Down) I might even consider extension cord type cable from vehicle battery to fans.
Fans are so low consumption a 14 Ga extension cord would do the job well with no worry from me,
And a running vehicle next to the house (outside) isn't ideal, but it beats freezing, and let's not forget thing in the home that can freeze...
Now, if you go the DIY route, and fix the issue before it becomes urgent/emergency...
Behind the facing for the fireplace will be an electric hook up for the fan.
I would install a plug in box if it didn't already have one so the fan plug can simply be moved to a back up power source, like small solar or standby battery/auxiliary power unit.
APU's come in all shapes, sizes, capabilities. From computer backups to industrial sized units.
Solar panels on garage or where ever, batteries & inverter on a wheeled cart.
Simply unplug from panels and take it in the house for use.
It will weigh as much as two large batteries, plus inverter or what ever else the maker hangs on it,
Or since I'm the DIY type, build it myself, nothing but panels, charger (charge controller) and batteries.
I got enough of gasoline & diesel generators real fast...
First, they SCREAM, or they are too small.
(Small might work for only the blower motor and a light or two)
Fuel goes bad and takes carb gaskets and fuel pump with it.
It didn't take me too long to convert to propane which never goes bad and doesn't rot the fuel system on the genset.
Propane is as portable as gasoline, never goes bad, contained in the tank until you open the valve, and most of us have propane powered hardware now, gas grills, etc so there is already tanks laying around.
That's just what I might do, not trying to tell anyone to do it in any way...