
For sure, all dogs will prefer to lie on a cool floor when the weather goes stupid hot. With our litters, we had two 4 X 4 sections, the one with pig rails round three sides and the other not. Puppies were in the pig-railed section, in a completely other part of the house and the floor (which was off the ground - and the sides were roughly 2.5 high) was covered with newspaper and with vet bedding over the top. Obviously outflow was minimal and dealt with by mum.
Once the litter was up and around and certainly by week 3, the original section was moved into the kitchen and the second 4 X 4 section added. That one had a hinged door. The whole floor was covered with layers of newspaper which was regularly changed, and anything that arrived when I was right there, picked up. As most of our litters were born into the better weather, we had an outside pen and they'd spend part of the waking day out there at which point I did a complete clean out of the whole box. It still got rather rank towards the time they went home! I couldn't have them running around out of the box (adults) however. So the box wasn't open, other than to let mum come and go.
I'm afraid it's just fact - having a litter of puppies means mess, and loads of WORK. Not for the faint-hearted which is why we only did litters when we needed the next generation. And why once they were all old enough to go to their new homes, those we weren't keeping, I was more than ready to see the little dears go!
ps Those we kept (usually 2, but once 3) went into a smaller area with a raised bed and tile floor - covered still, with newspaper. We have never used pee pads.