Thank you for your question and your kind review! If you, and others, live in northern climates where it is cold in the winter and are concerned about your bird, consider the following:
When normally feathered, bird feathers are amazingingly insulating and can protect against wide swings in temperature. That is unless the feathers become waterlogged in which case, the bird can become cold very quickly. This is a good reason to NOT use products, like some shampoos and soaps, that completely soak the feathers.
If your bird is not normally feathered, such as with feather damaging behavior, skin wounds or other causes that leave skin exposed, then cold and heat stress are more likely.
If your bird is sick, it may not be able to handle cold or heat stress as well as would a normal animal.
A cold bird often shivers.

Keeping these in mind, if your bird is healthy and seems comfortable after a shower it will probably be fine at room temperature (65-75 F). If you are concerned and still want to bathe your bird, then gently dry the bird and give him/her the option to set next to a heat source. If the bird is cold, he/she will more towards the heat (or away if too warm).

M. Scott Echols, DVM, Dipl ABVP (Avian Practice)