Thats a really odd one.
Generally that I know of, a furnace should not interfere that way.
That its metal, etc in itself would cause some just being say directly on the opposite side of it.
But that property should not change from it being off/on.
The motor running.. yes there should be a bit more of a EM fields on it.. but again, that SHOULDNT interfere, its by default not using anything near the frequency range that wifi runs on.
does the furnace have a wifi thermostat? Is that anywhere near the modem/pod??
Wonder if when its talking its causing too much interference? (it shouldnt tho, as its usually more just a router type device which would have interference due to stronger antennas).
Does the modem itself stay up when it comes on? and just the wifi drops?
Wonder if something like the furnace and your modem is on the same power breaker and somehow when there is the more draw for the furnace when it comes on that its taking power from the modem??