Empire Heating System model FAW55IP
Interesting model.  Empire furnaces are tremendous because they run without any electricity at all.  I really dislike that this one needs electricity to ignite (thus: useless in an outage), but maybe it can be made to work on a solar/battery system, in which case, good riddance pilot.  For that matter, the ignition current is tiny, and could itself be supplied by a local battery topped up from the thermocouple.  Who knows.  

On any Empire furnace (pilot or electronic), the furnace is fundamentally a convection unit. The fan is a "bolt-on" and is merely to distribute heat more effectively.  On one of my Empires, if the power fails, simply, the fan doesn't run, the heater still heats the house.  Also, the fan "trails" firing and quitting of the gas burner, only removing heat when the heat exchanger is hot enough to require it.  

In your case, the fan sputters on/off due to an effect called "heat soak".  It efficiently cools the outside of the heat exchanger, but the inside is hotter.  When the fan shuts off, heat is still coming out of the heat exchanger.  That heat raises the temperature of the heat exchanger skin, which causes the fan to start up again.  Rinse wash repeat until temperatures equalize.  

But I would expect fan or its thermo-switch design to account for that.  You may have a defect in the thermo-switch, or it may be misinstalled. The fan may have a delay circuit which is defective.