Birds can't catch a cold, so anything they get is almost always treatable in some way.
You may want to invest in a ceramic heat bulb. You can often buy them from pet stores in the reptile section, and these give off no light! I use one for my bourke parakeet, and have it placed in such a way that she can determine how much, if any, additional heat she wants. Sometimes she likes to sit right under or next to the heat source, which warms her body, other times she avoids the heat.
Happy huts aren't recommended for cockatiels, as they usually view anything dark as a nest if they use it.
Here's hoping she feels better!!