Buy a maximum temperature thermometer, available from stores selling weather measuring equipment
http://premiergreenhouses.safeshopper.com/12/56.htm?341 , and place it in the top of the shaft for one week. Let me know what the highest temperature recorded was. I will try to figure out from that what the conducter size and type will need to be for your installation. One critical issue is the type of conduit you use. Electro metallic tubing would be a good choice. You have to be able to install the conduit in such a way that you can keep it's entire length away from the chimney surface itself. If you can not provide support every ten feet of tubing then you can not use conduit. One possibility is to run the tubing on the outside of the chase on the exterior of the building. In that application you could be sure that the ampacity for three current carrying conductors in conduit in free air would apply.
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Tom
