In terms of general handling, you won't melt the plastic (those honors happen automatically with rubber and some pvc whether you handle them or not!) but there are some rules of thumb I've discovered over the years.
When you handle any figure, be sure to avoid touching decal surfaces, as the image can actually rub away over time. Seriously avoid contact with any chrome parts, as finger oils can positively cause blackening and discoloration, and in this day and age with slip-shod chroming could also accelerate chrome peeling.
Overall, I try to also avoid painted surfaces, especially chalky, matte finishes, as the paint is more prone to wearing off than glossy coatings.
I try to handle my figures by the unpainted plastic parts where at all possible. It's not going to always BE possible to avoid touching certain surfaces, especially when transforming, but handling the aforementioned parts with kid gloves will go a long way towards avoiding damage.
Hope that helps!