I apologize that no one has responded to your question sooner. Different experts come online at various times. I just came online and saw your question. I'm sorry to hear that your dragon is not doing well.
In a cold-blooded animal, the lack of heat in an injury doesn't mean anything. There is no internal source of heat in the body, so an injury will not warm up. The swelling may be the result of a broken bone or an abscess (infection). It would be impossible to tell based only on an online description. The best thing to do would be to take your dragon to a reptile vet to be examined and to have x-rays (radiographs) taken. This link will take you to a directory of UK reptile vets:
If the leg is broken, it may be the result of Metabolic Bone Disease (MBD). MBD is common in captive beardies because pet stores give out incorrect information on lighting. Besides a basking light,it's extremely important that dragons have a light that produces UVB rays. A Reptisun 10.0 is a good brand that does. If you choose another brand be absolutely certain it provides UVB rays. Don't take the word of pet store personnel, but read it for yourself. Full-spectrum, DayGlo, daylight, UV, and UVA are NOT the same thing. I'm putting a lot of emphasis on this because it's crucial to a reptile’s health. Without this light, Metabolic Bone Disease (MBD) will develop because they won't be able to produce vitamin D. Vitamin supplements are not a good replacement for the proper lighting. MBD causes a very slow and painful death. UVB bulbs must be replaced every six months as they lose their effectiveness after that, even though they may still look fine. Light that comes through a window isn't sufficient because the glass filters out the UVB rays. If proper lighting has been provided, broken bones can still occur as a result of a fall.
If you have more questions, let me know by clicking on REPLY. I hope your beardie will recover uneventfully.
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