Yes they can. I am so worried about that. I make sure he has shade and a dripper and then I set my timer for 15 mins and bring him back in till he gets older and stronger. I did this with my other cham, we sort of built up to a longer sun time till he got older. Now my older cham lets me know when he is ready to come in by going to the little door in his sun cage, usually about 45 mins to and hour. I am a nervous mama, so I keep an eye on them the entire time.