MORE INFO: we have been in the attic more often thus opening access to the attic from house and garage. We also added an access hatch from the attached garage so the access is easier, instead of crawling into a small closet and then up into a small hatch on top of the coat rack. We could seal the garage hatch door with weather-stripping to minimize the airflow from the occasionally heated garage to help with the frost? That access door is fire rated.
Can insulation (rigid foam) be added to the chase from the inside. The top of the chase does not have enough overhang to add insulation to outside surfaces under the siding.
Contractor said insulating the chase would be the same as insulating my roof sheathing in an insulated unheated attic.
1st picture of inside of chase at install

2nd picture of chase prior to siding waiting for the chimney
