Double or triple wall pipe?

Couldn't find anything in search about this particular question so I bow to those brighter than me.
My house has a brick w/ clay flue chimney 12x12 on the east end 10 ft. tall. Dad and I originally built the house for a open fireplace but the mason that did the brick/block work talked Dad into making it for a stove to reduce heat loss. Hearth is inset with a 1/4 in. 3'x3' steel plate at the base and the flue stacked above wrapped in brick.
Had a Fisher type stove w/ 8" pipe running the 18" through the plate and into the flue straight up. Wish I had that stove still but it,s gone. I got a Bosca fs500 in there last winter(saved our butts) set up the same way. Made a reducer plate to 6", But it became a creosote monster. Too little exhaust in too big a flue plus -20 temps cooling the brick. Time for a ridged liner. Drop it straight down in the flue, setting on the steel plate. Make a collar to hold the top square and vent the opening and a top plate on the crown.
Will double wall class A be too hot on the outside pipe and cause condensation? I have all kinds of room in the flue for triple wall and it seems to me the outside would be cooler. I don't want to warm up the inside of the flue enough to cause the brick or clay to sweat.
Thoughts? Am I being a wuss?

DAKSY said:

Class A Chimney is not designed for your application. Most of us here will probably recommend a 6" rigid or flexible stainless steel liner with an insulation wrap. A top plate is attached to the higher end of the liner & is also used to seal the 12x12 terra cotta flue at the top. The cap attaches to that plate.

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Thank you for the reply. I understand that but isn't a class A the same thing? 22ga. inside pipe, insulation and an extra ss pipe outside for added rigidity. Plus 2x is cheaper than liner pipe and insulation. 3x is about the same money. Still have to buy the bottom fitting to attach to stove pipe and a cap. I can make everything else. Even have a chunk of copper roofing saved for such a use. My concern is keeping a warm pipe or liner from creating condensation in the old flu given how cold the brick will be.

Prices from a near by chimney supply. Liner,$120 for 3ft. section; insulation,$33 for 2ft. piece=$153+tax. Metabestos pipe,$137 a 3ft. section. Sixteen bucks isn't the issue but the durability over time.

Thank you for your concern for my family's safety. Rest assured nobody is more concerned than I. I came here to ask a question I didn't have an answer to. Still haven't found one. Is condensation more likely with class A than liner and insulation, or will the gap at the top take care of any that may accumulate?

The question was condensation between the clay flue and ANY pipe. Called Rockford, said the 1/2" gap under the top plate would vent any condensation, 11ft" of metabestose on the way. Thanks for your thoughts all.