How old is the chick?
Young Chicks have fluff, which really doesn’t do much to keep in heat. You can wash an older chicken, which I’ve done before. Even with an older chicken, you will need to use a blow dryer to dry the underlying fluff.
If you NEEDED to wash a chick -like some strange combo of events that caused the chick to need a cleaning, then I’d use warm water. If soap was needed, then a very MILD and UN-scented soap. I have used (on adult chickens) very mild/low sudsing baby bottle detergent. I tested it before hand to verify it was low sudsing and rinsed off/out easily. Chickens have sensitive respiratory systems, so fragrance should never be used with chickens. At the point the chick is clean, wrap Immediately in a fluffy towel and blot as much moisture as possible. Use a blow dryer to get mostly dry, but keep your hand in the air flow to verify it is not too hot and use the low/warm setting. For this task, with a chick, I’d be inclined to use a heat lamp to place the chick under (I usually use heat plates in the day-to-day raising of chicks) so it can have more radiant heat heating up the general area. If you are careful it could be done. However, it is not recommended as a recreation activity bc it would be stressful for a chick.