We went to my wife's family's cabin in Wisconsin last week, and I had to bring the beardies along for the ride.
I brought them outside to bask, since I didn't bring any UV light, and mostly because I find it's a great Psych picker-upper.
I AM NOT NECESSARILY RECOMMENDING THIS, BUT THIS IS WHAT I DID.
I had to constantly watch the temps in the tank and cover part of it sometimes, because of high temps.
Two things seemed to work: Setting the 10 gallon under trees so it would only get partial sunlight; or setting a towel over 1/3 of the tank so they could go to the cool side if they wanted.
I also occasionally would drip water on them, to force them to cool off a little bit, and allow them to drink if they were thirsty.
For a somewhat grown beardie, he may not have had a good cool spot to go to in a 10 gallon tank.
If you had the beardie in a 10 gallon in full sun, for more than 10 minutes, and weren't monitoring the temperature in there, I would say he may well have cooked. Perhaps he was already dehydrated from soupy poopies, and wasn't in a condition to handle quite that hot of a bask.
Again, I don't have much experience doing this, so I was taking measurements and watching closely, and using water to cool them off occasionally.
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ETChipotle