If I ever move to the country I might try this!
Bonus video of a Korean Gardener who grew carrots on his patio in discarded Plastic Bags. You work with what you have! Kudos to him!
How to grow carrots in Plastic bags...Korean Gardener
I believe he is using a Shin Kuroda carrot which is fairly heat tolerant and a stubby like Chantaray.
Botanical Interests....Shin Kuroda Carrot Seeds
"Late planting your garden? 'Shin Kuroda' is quite heat resistant, so don't hesitate to sow in late spring, and even into the summer (when you might be doubtful about sowing carrots). Shin means "new" in Japanese, which alludes to its improved, tapered, 5"-long roots with wide shoulders, that grow through heavy soils with ease. Simply unsurpassed for flavor—one of the sweetest carrots you will eat!"
More information on this carrot from Northwest Meadows Conservationscape:
"The Hon-Kuroda is one of the original foundational carrots to emerge from Nagasaki prefecture’s acclaimed Kuroda Gosun Breeding Society in the 1930s.
Centered around the Kuromaru-cho neighborhood of Omura City, a group of farmer-vegetable breeders conducted continuous crossing efforts between different carrot varieties to arrive at this superior type – a sweet, orange-red carrot, with very little tapering, setting a new global standard for what a carrot could be.
Extremely high in beta carotene, the Hon-Kuroda is extraordinarily adaptable to different soil types. It is very heat tolerant, has vigorous growth, and is excellent for continuous planting. (Sow an additional row every two weeks from May to August for continuous season-long harvests). If you have room in the garden for one carrot, this should be it."