How can I prevent rubber handlebar grips from melting/disintegrating? I bought a used mountain bike recently that came with some not so great handlebar grips.  In humid weather they get really sticky (so much it hurts to pry my hands off them) and bits of rubber come off and stick to my hands.

I'm replacing them as soon as I can but in the meantime I'd like to know what I can do to prevent this from happening with my new set of handlebar grips.  Does this happen when you leave your bike in the sun or the rain?  Is it inevitable after a certain amount of time?  Is there anything I can do about it?
I remember this would happen to me as a kid while on my bmx bike especially in humid summer weather. 

So you are buying new grips already - I'd say make sure they are a harder compound than whatever your current ones are. Seems like harder rubber is less likely to deform/melt away. 

With your current grips you might try wrapping them in bar tape. There are many kinds. I use cork - is good for wicking away moisture from sweaty hands but it is thick. Synthetic bar tape that's thinner might wrap tighter and be less bulky around your grips. If you don't have any bar tape, maybe try the clear plastic wrap from your kitchen. It should keeps the little bits off your hands. Could be more slippery so be careful.