Bearded Dragon Behaviour
The most common reason for an open mouth is that your bearded dragon is regulating his/her temperature. Unlike people, bearded dragons cannot sweat, therefore to control their body temperature they will open their mouth whenever they reach their ideal body temperature and don’t want to get any hotter. Normally the bearded dragons will do this when they are basking under the heat lamp.
Bearded dragons will also have their mouth open if they have a respiratory disease. However, since having an open mouth is common behavior for bearded dragons, it’s normally just a sign that they are regulating their heat.