Watching out for cold sensitivity is a big one - my poor little Wigglet gets chilly fast! I try to keep her with lots of furry hammocks and ones with pockets so that she can have a 'blanket' of sorts to retain heat. I notice that she eats way more too, and I think part of it might be all the energy she burns just keeping her little body warm.
I do occasionally give her a bath. She hates it, but I notice that she's not really as clean (or as clean smelling) as her furry boyfriend. She has respiratory issues, so I worry her own body odour could irritate her nose! I just run water in the bathtub up to her knees and gently wash her with sensitive skin face wash. After she gets a BIG towelled cuddle and I moisturise her with organic natural face cream - her skin gets dry!
Definitely be prepared for skin issues. She gets 'pimples' (it's a blocked gland) over her eye quite a lot and it can get quite big and painful looking. I took her to the vet for it once when it looked bigger than I was comfortable with, and he said not to worry - he could lance it, but it'd probably go away on its own (it did). If you want to speed it up, you can put a warm compress over it. Any skin complaints not in sensitive areas like eyes shouldn't really be a problem though, just like pimples don't really bother us much aside from cosmetic concerns.
Whenever she gets scratches (her boyfriend can be a bit of a bully sometimes!), I try to watch them really carefully and keep her clean because of the risk of infection. They get more injuries to begin with, plus there is no fur to protect her skin from coming in contact with fecal matter, etc. On top of that, double rexes often have very compromised immune systems because they have been so inbred - so abscesses are a worry! Mine has never had one.
Lastly, watch out for resp issues. My poor Wigglet has been on antibiotics for over a year now with chronic resp infections that she just can't fight off - the antibiotics keep it under control, but she is a snuffly breather and has porphy eyes. According to my vet, this is often a part of having naked rats. It's really important to keep their cage SUPER CLEAN, because the smell irritates their nose so much - and they can smell so much more than we can. A humidifier near the cage seems to help her breathing too.
I love my naked little rat - she is so weird-looking and special. My vet once told me he thinks the gene tied to their nakedness might also be tied to their disposition - he says they are usually much more friendly and less fearful than other rats.
