What is the best way to move these kittens?

My cat had kittens yesterday and is doing great with them, She feeds them and is very attentive when they cry for her but she moved them from the place she gave birth to them and under my nieces bed..Now it isnt so bad but it keeps my niece up at night with the mewing and the floor is wood so i imagine its not very warm for the little kittens..So we went out and got a large cardboard box and set it against a corner where its semi isolated and stuffed some thin but warm blankets in it and set mama cats food and water in front of it and we planned on moving the kittens but i need to know the best way to do this and make my cat comfy and the kittens more safe than a cold wood floor