yes, puppies can't control their body temperature until they are 2 weeks old, so keeping them in a warmer room is the best, and get rid of the plastic tub the walls are too tall that is why she is dragging the babies to the floor, I never liked using those under the bed containers for that reason. do you have a crate that you can remove the door and use it like I have? or anything with a lower wall? she is going to need a pee pad in there and her food and water..
make sure you give her her dose of calcium before you go too , is very important now that she is lactating the babies..
if worse come to worse, take a cardboard box and cut the walls to about 3 inches from the bottom and line it with warm blankets and use that for the day.. is better than the plastic container.
hugs,