Greg's 3-way switch and inlet solves that problem quite nicely.

Something like this would be perfect because it could replace the On-Off
switch currently installed on the furnace.
That's the way I'd do it if I didn't have a transfer
switch/interlock at the panel.. Just switch the live from the panel to
the genset, and leave everything else connected. My brother did that
ay his place - he plugs the "house extention cord" into the generator.
It has 4 or 5 outlets strategically located around the house to plug
things into, and a 3 way switch on the furnace. - all hard-wired - no
extention cords inside the house - and theconnection to the house is
the same as the connection to his travel trailer.


Some folks might even backfeed the whole panel
through the clothes dryer receptacle - allowing the generator to
supply their well pump, sump pump, freezer, etc
... as well as the furnace. Selectively - by opening & closing
the panel breakers.
Of course they always remember to open the main breaker first
and close it last, after the generator is shut off.
John T.