Usually blowing bubbles from the mouth which appears as foam is a possible indicator of heat stress. We have seen this situation in the heat of Florida while capturing swans. Usually, this dissipates just as quickly as the onset once the bird cools.

How old is the cygnet? This is an important issue because you don't want to take a very young cygnet (few weeks of age) from its parents for any significant amount of time as the parents may reject the bird and/or cause more stress. If it is an older cygnet (months) you can use a water hose with cool water and dowse the bird. Let it preen dry and then place it back with the parents. Make sure it is dry so that it regains its water repellency. This is also relevant to the age as very young cygnets do not have water repellency and you may risk drowning the cygnet.

Has this behavior been occurring for several hours or days, is the bird gasping for air or acting otherwise abnormal: constantly shaking its head, drooping eyes, not eating or pooping, not staying with the group or the parents shunning it, does it have a continual gaping mouth (looks like it is panting all the time)? If any of the signs are present or you still have concerns, get the cygnet to a licensed avian/waterfowl veterinarian quickly. Please let us know how this situation progresses. The Regal Swan