DO what dbduck said: lay a cheap thermometer there. THEN place a cheap empty shell (Athearn undecorated) at the closest spot. You then have two point’'s of reference: HOW hot, and TOO hot.
If you are not going to park trains there, the only conceivable damage is to the PLASTIC TIES on the track affecting alignment. (Substitute WOOD roadbed? - True Scale from Trout Creek Engineering makes excellent Ready Track). The wood won’t melt and the rail will dissipate the heat. Law’s of Physic’s, you know.
CBQ - That two inch figure may be posted on the side of the burn but it would never be accepted under the NFPA Codes…or by your insurance company. It’s been a while for me but the NFPA used to require an absolute minimum of 18" horizontally and, depending on the type of furance, it could be up to 36", for any combustible material storage.
There’s also a phenomenon called pyrolizing, in which a combustible surface, subjected to fairly modest heating over a very long period, will eventually self ignite. So the best route for SMS to follow is call his local fire/building inspector and ask.
Look in the operating manual for your service. It gives required clearnces. The manual for my furnace, 5 years old, says it is approved for closet installation. For the sides and rear, the clearance is only 1 inch. The front should be unobstrcuted so as to not interfer with the combustion air intake. It says to have at least 2 feet in the front for service. Your furnace may, of course, be different. Also, as others have said, local building codes (and insurance) may have different requirements.
I wouldn’t take any chances getting too close to the exhaust flue of the furnace or water heater. And as someone who has worked servicing both, I can tell you that time spent making any “interfering” railroad sections removable will be well-spent. The moment the ballast glue, scenery paint, and/or foliage dries, something will happen to the house’s “physical plant”, and you’ll be wondering why the intercourse you didn’t plan better. Murphy created a whole slew of laws covering that!
I think I would avoid the furnace area, by several feet.
What would you need to do when the furnace needs servicing, parts, repairs, or in the worst case scenerio… you need to replace the furnace completely… would you have enough room to remove the old, lift / cram it out, and install the new ? Your railroad could be out of commission for days, weeks…
others have gone closer, and I’ve seen some very creative layouts, but I’m not interested in being superman, I’d rather enjoy this super hobby, and keep it less complicated. Trains will run almost anywhere… happy hobbying
also, don’t get too close to the tub (same reasons) [:D]