Winter Wood Stove Chimney becomes Summer Vent Stack?

I just had an amazing idea and I cannot believe no one has thought of it before...so maybe I am missing a major flaw in my thinking..
When it is cold - Wood stove chimney pipe AND When it gets warm - passive vent stack. interchangeable!
I have a great big wood cook stove in the house, complete with fancy double walled pipe leading up from my ceiling through my attic and 6' above my ridgeline. I have a standard cap on this pipe, that I remove every summer to clean the chimney. The stove isn't used between May and September...as it is too hot. What if I modified a whirlybird ventilation twirly to connect to the top wood stove pipe in the same way as the wood stove cap. Then, in June, when it starts to get hot, I disconnect the inner stove pipes (stove isn't used anyways), perhaps add a screen at ceiling level, maybe cover the stove itself and switch the cap for the whirlybird. Voila. One pipe, two uses. It would suck all the hot air out of my house and vent it out the chimney... Would this not be tickity boo?? Why don't I find anything on google?
I don't think condensation would be an issue if it was only used in the hot months, it would go back to being a smokestack as soon as it got cool...
What are your thoughts??
Thankyou
Meagan

This has been done many times. It works best if there's lots of dark colored chimney above roof line.

For best results, it's good to have a chimney made out of heavy material. It's can heat up all day in the sun, when the vent is closed. Then at night, when the outside air is cooler, open the vent and allow the chimney effect to send warm air up that will be replaced by cold air that flows in the windows.

The best example of this that I know of, are large stone chimneys in India and Pakistan that use dark painted masonry chimneys to power the system.

No need for the whirlybird. They're more of a restriction than a benefit.
A column of warm air such as in the pipe already has quite a bit of energy stored, all you need is to give it a place to go - up.  An extra 3 ft of pipe would do more than the whirlybird.

Yes I agree that many people have implemented and used vent pipes such as this...I hadn't thought of them as the same as the stove pipes! Thanks for affirming my idea! Its a great idea to paint it black...I shall have to look into why stove pipes are sparkly metal colored. My summer idea has to meld with my winter necessity of stove pipes.
Hmmm...If I didn't have a whirlybird, I'd need to leave the stove pipe cap on to keep out the rain. And I'd have to screen the top, or the bugs would get in. The whirlybird would at least ensure nothing would come down the pipe

I shall have to look into why stove pipes are sparkly metal colored.

The shiny metal pipes are likely stainless steel, and if I'm imagining it right they are probably of the insulated variety, which are great for stove pipes exiting the house exhausting smoke with minimal creosote build up at the cold transition zone, but not so great for gaining heat through sunlight for aiding upward venting of air.  That may not be the case if the pipes are uninsulated, but the double walls you mention

 fancy double walled pipe leading up from my ceiling through my attic and 6' above my ridgeline.

made me think of the insulated stuff, and even without the insulation, the double walls will take away from their potential to radiate heat internally.  At any rate, if you are going to paint the pipes black be sure to use heat resistant paint; they make it for wood stoves and pipes--if you don't the paint will not last long, and will be burned off in a toxic chemical release.