A thermometer....
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On the inside of one of the removable panels
On the inside of the blower panel door.
If you mean where can you find it, look on the inside of one of the cabinet covers or the control box cover of the furnace.
Provided your furnace has a humidifier on it, you may replace the filter. I would recommend going to a local home improvement store to find the model that will fit your furnace. If you do not currently have a humidifier on your furnace I would recommend contacting a local furnace supply company to enquire about a new furnace or upgrade.
I would think the question would be how do you find the parts for a sixty year old furnace. You are right, but that got me nowhere. So I am looking for someone who knows the answer to that question!
Usually the filter is right on the inside of where the return air duct meets with the furnace. You usually have to take off the side or front panels of the furnace to gain access to where the filter is. Usually these involve sliding them up and out but it can vary. Check an online owners manual for the make and model of your furnace. Usually there will be a plate of information somewhere on the casing of the furnace with this information.
One site for furnace parts is actually furnaceparts.com. Never would have guessed that. You could also try .AllPartsHeating.com.
There are many places to find gas furnace prices. One can look on sites like Furnace Price Guides, Century Gas Furnace, and Consumer Reports. One can also find gas furnace prices by going to a local heating supply store.
In a furnace troubleshooting chart, you can find information on common furnace problems, possible causes, and steps to diagnose and fix issues with your furnace. This chart can help you identify the problem with your furnace and guide you on how to resolve it effectively.
You can find a schematic for a gas furnace on the website, Uncionradio.
The model lable is usually located on the inside wall, just above the burners, on the left. You would have to remove the panel that has louvers in it, to see it. If the entire cabinet were missing, you may never find out.