First off, welcome to the forum!
In regards to temperature, if your normal temperature is around 30 you may need a place in the tank that's closer to the low/mid 20s where she can avoid the high temperatures. And 32 is still a bit low for her hot spot. If you could give her a spot of 35-40 that's where she could go to digest her meals.
In regards to when it's safe to handle, 5 days would be about my minimum settle-in time. If she's hiding a lot, maybe give her more time to settle in and get used to everything. If she's active, alert and seems curious then go ahead and introduce yourself.
Skinks can bite, but they'll usually give you lots of warning first. The first thing you may get is a huff, which is a closed-mouth puff of air. This isn't really defensive, just the skink making itself known. If the skink is scared she may hiss, which is open-mouthed. She may show off her blue tongue to scare you away. These are signs she doesn't want to be touched, so back off and let her get to know you on her own terms. Maybe leave your hand in the tank and see if she wants to explore it.
If she does bite, it might hurt but it's not too bad IMO. The smaller they are the less it hurts. Mostly they just bite and let go right away; a warning to back off. She won't hurt herself.
If she's alright with you approaching you can see if she'll climb onto your hands or you can pick her up. When picking up/holding a skink the most important thing is to support the legs. I generally pick up my skinks around their back legs then put my other hand under their front legs. Never pull or grab a skink by the tail, since that can come off. Skinks like to feel supported and may flail if they think they're going to fall.
This is a video of me picking up my most aggressive BTS. I don't hold him for long since he's not friendly, but you can see how he reacts and how I pick him up:
http://youtu.be/dHv9wiRr0iE
Once you get her out let her explore you and other safe areas. You can offer delicious treats like mango when she's out as a way of teaching her coming out is awesome. She may want to explore, or hide, or just relax with you; every skink is different.
Be patient and enjoy learning all about your new friend
