Hmm.. Well first of all, he should have a reptisun 10.0 TUBE, not coil. The coil UVBs have be known to cause eye problems as well as not provide bearded dragons with the correct UVB. You should get a reptisun 10.0 TUBE as soon as possible! Most stores should carry them. I think most people would tell you to turn off the UVB coil as its more harmful than anything. If its warm out, you can take him outside for natural UVB, just make sure he has shade to hide under in case he wants to get out of the sun for a bit. And don't leave him unsupervised, obviously, lol
Also, how old is your beardie? 10 gallons is probably too small for him.. Also, he should not be fed mealworms at all, especially if he's young because it can cause impaction. Gut loaded crickets or dubia roaches would be a better choice. Is he being offered any greens?
I'm not 100% sure about the temperatures, a quick search on this forum will help you find the information you need but I believe it needs to be at least 95 degrees Fahrenheit for them to digest properly.
This is all great info.
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For a young dragon, his temps should be 105 to 110, but 95 is the minimum for healthy digestion.
It's really advisable to upgrade his tank, and even if he's small a 10 gallon tank usually doesn't hold the proper temperature gradiant.
Phoenix worms and silkworms are also excellent staple feeders that can be purchased in appropriate sizes.
Many people feed their babies phoenix worms. They are full of calcium and nutrients, and don't need to be dusted with crickets. Dubia are also a good staple feeder, though depending where you're located, may not be possible to aquire.
What type of thermometer are you using? A digital thermometer with a wire probe or an infrared temp gun are really the only acurate thermometers available.
Your baby is most likely still suffering from some relocation stress. That doubled with the coil UVB is probably why he is not eating. I would agress that you should switch off the coil now, and aquire a ReptiSun tube asap.
If you have the receipt, you may still be able to return your coil bulb.
Baths are good.
Bathing him 3-4 times per week will help to keep him
hydrated. Babies in particular tend to dehydrate quickly with their higher temps.