Is your furnace 3 phase or single phase?
Can you please post the specs. of your generator.
If it is a diesel/fuel generator it will probably have a clean sinusoidal signal while running (very low THD).
The problems will probably be when you switch it on and off.
Doing that willingly you should disconnect the furnace/generator load switch before you do.
But think about the case it runs out of fuel and dies out while the furnace is still connected to it...
You have nothing to fear about connecting to a PC line-in.
It is quit simple anyone can do it.
Here is how in your case:
If you have a small,low power 120 to 12V AC Transformer (any low voltage will do 3VAC-18VAC or so ) .
It needs to be AC(not DC!) and not an "electronic one",
simply a pure transformer.
There are wall-warts like that available or "bare transformers",in case you need to buy one(for almost nothing).
Connect like this:
View attachment 25703
Can you please provide some more detail on the wiring diagram of the 3.5mm plug ?, just to be sure, Thank you, Jim