If they are being fed and aren't overheating due to an improperly hot environment, they should not get dehydrated. I can't say with 100% certainty that dehydration couldn't occur as the result of a medical condition despite being properly cared for by mom and breeder, though. With any animal, you can check for dehydration by doing a "tent test" (gently pulling up the skin between the shoulder blades and checking to see if it goes back to normal at an appropriate rate); however, I don't know whether or not there are any safety concerns with trying this on a newborn kit. Unless someone can chime in to say that it's definitely safe, I wouldn't do it if there's no reason to suspect dehydration.
60F is highly unlikely to cause overheating (though it's not impossible) - that's lower than most people like to keep their houses in the winter (but sounds just right for me!).
If you still don't see well-fed tummies when you're ready to go to bed, you should try to hold the doe and put the kits to her to nurse - sometimes this helps first time moms get the hang of what they're supposed to do (it may take doing this for a few feedings in a row before she starts nursing them on her own). It sounds like you have a good relationship with your rabbits - when the doe trusts you and is comfortable with you handling her, she's much more likely to let you hold kits to her to nurse.
If mom absolutely won't nurse them even with you intervening, then things get tricky. Ideally, you would use another doe who has a litter of her own that's being properly cared for as a surrogate (it's ok if her kits are as much as a couple weeks older than the rejected litter). To do this, you remove the surrogate-to-be from her cage/hutch and move her to another location, then add the rejected kits to her nest box. You'll want to keep her away for an hour or two so that the two litters of kits can wriggle around together, allowing their smells to rub off on each other so they all smell fairly similar. After that, add mom back to the cage/hutch and leave them be. Surrogacy done in this fashion has an *extremely* high success rate - the doe almost never rejects the "foreign" kits.
Unfortunately, if surrogacy is not an option then your odds of keeping the kits alive is very slim - even experts have little success hand-raising extremely young kits, as a mother rabbit's milk is exceptionally rich and virtually impossible to reasonably duplicate. Here are some sites with good information on hand-raising orphaned or rejected kits:
http://www.mybunny.org/info/newborn.htm
http://www3.telus.net/raisinghouserabbits/orphans.htm
http://www.rabbit.org/faq/sections/orphan.html
http://www.2ndchance.info/bunnies.htm
Even if you do manage to successfully hand-raise them, they still count as a failed attempt at parenting for mom since she didn't do it herself. Most breeders (and not just of rabbits) use a "three strikes" rule for their breeding stock - rejecting or killing the first or even second litter (or baby) is pretty common but if a doe (or parents, in some animals) fails to raise her babies successfully on her own three times in a row, she's often deemed an unfit parent and retired from breeding.