She honestly doesn't look sick to me. Her eyes are clear, her poop looks normal and she appears alert and active when she's not napping. BOs are fluffy chickens and mine looked just like yours when roosting unless they were hot.
It's not uncommon for chickens to take light naps during the day and sounds that they've grown accustomed to don't normally phase them. Mine like to sit on the outside roost in the sun during the day and get a snooze in while I mow the lawn and they don't crack an eye open. A healthy looking chicken who suddenly starts doing deep naps during the day is an indication that it didn't sleep at night. If all was good before you changed the bulb, then it's likely the light that's keeping your little one awake at night.
As for the heat lamp, I think the rule of thumb is if they are fully feathered, they can insulate themselves. If removing the heat worries you, you can try doing it gradually by moving the lamp up a foot every night until you've weaned them off. 20F is not that cold for a chicken. It might make you feel better to know that I don't supplement heat for healthy chickens unless the inside of my coop reaches -20F.