Rusty Stove Pipe Mystery

We replaced our airtight sheet metal no-longer-legal-but superior stove with a "modern" contrivance (stove) because age took its toll ie it burned out. With the new "modern" contrivance (stove) we then got a big rust streak down each side of the roof below the stack. Oxalic acid removed the stain but we never had that happen for the 25 years we used the airtight no-longer-legal-but superior stove.

What was rusting? Detailed investigation revealed that the inside top 1/2 portion of the single walled stack between the stove and ceiling is rusty; about 2 feet. The triple walled pipe thru the ceiling/attic is not rusty.

Certainly one of the products of combustion is water. Of course the wood is not perfectly dry - it is dryed in 100º heat most of the summer - but absorbs some moisture from the air even tho its stored in a shed. So that's the source of the water. The said water must condense on the inside of the pipe to cause it to rust. For that to happen the temp of the pipe must be below the dewpoint of the water in the hot xost gases rising from the stove. How can that be?

I often at bedtime throw in a relatively large bunk log, get it burning then damper the stove down for overnight. In the morning the house is warm but the pipe is or may be touchable - you can lay a hand on it. The stove likewise. The log is sometimes gone and sometimes there is still some of it left.

I believe it is during this cooler operation that the condensation and rust formation occurs. I believe it did not occur with the airtight no-longer-legal-but-superior stove because it had an automatic damper which would be wide open in the morning. That is, it would open as the stove cooled, increasing air flow and preventing the relatively incomplete combustion and lower xost gas temperature which must occur in the "modern" contrivance (stove) with its non-automatic damper.

There must be a temperature gradient up the pipe. The single wall pipe radiates to the room and cools. The top 1/2 is coolest. The triple wall pipe inner surface thru the roof probly stays hotter the whole time since it is shielded by the 2 outer walls.

So it would seem that the most practicable solution to prevent rust is the use a double wall pipe from the stove to the ceiling thus shielding the inner wall and allowing it to stay (hopefully) hot enough that condesation does not occur. A caveat is that we'd not get the heat previously radiated from the 1-walled pipe.

Is my analysis valid? Is there another solution? Waddaythink?