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You might want to use an infrared light instead of a black light. You can get a variety of infrared heat bulbs in the reptile section of most large pet stores. (The PetSmart stores in my area have a bunch of them.) Two week old chicks are still pretty small, and near-freezing temperatures are cold. I just put out all of my chicks, ranging from just over a week old to five weeks old, but I gave them a large Premier Heat Plate ("electric hen") (similar to an EcoGlow brooder but the leg height is easier to adjust), and I also gave them a 100W heat lamp that is set to come on when it gets dark. Soon I will switch the heat lamp over to a thermostat so it comes on when the temperature goes below 70. Fortunately my chicks are now in a large enough area they can get away from the heat if it is too much. I would be worried about them in the cold, though.
My broodies sit on their chicks at night until the chicks are about 6 weeks old, even when it is relatively warm out.
Link to the Premier brooder (aka "heat plate"):
https://www.premier1supplies.com/c/poultry-supplies/heating-plates-and-covers
Good luck!