I want to get a generator just to run my furnace fan if the power goes
out during the winter. We are in the Boston area, and the snowstorms
are pretty fierce. I know that 3750kw will be plenty of power for what
I need, but is this as simple as running the generator outside, running
an extension cord into the basement and plugging my furnace fan into
it. Or I guess, plugging everything in, and then starting teh
generator.

Does the generator run even when no power is being drawn from it. Also,
would the thermostat work without power? What about the furnace itself?

Of course the generator runs even when no power is being drawn from it; does
your car motor run at traffic lights?
The thermostat normally draws power from the furnace, so if you hook it up
properly there should be no problem.
Furnaces can be forced to run without power, but without the fan running you
will trash it pretty fast.
Running an extension cord is certainly the cheapest and most idiot proof way
to go, but also the most clumsy. Your furnace probably doesn't have a plug
on it; you will have to do something about that, and I suspect you are not
the person to do it.
My furnace will run on a 500w generator; yours might not. Investigate that
before buying one.
Furnaces have been ruined by poor quality electricity coming off cheap
generators; but a lot of people do it without any problems. A judgement
call.