In the picture above it looks like they are all huddled away from the heat plate which tells me the heat plate is too hot.
I would suggest not stressing about added heat especially since they are inside your unair conditioned house.
You can leave the heat plate in there but I would pull it...
Take the plastic white part of the waterer off and turn it upside down.
Fill it with water and while it's still upside down twist the red bottom part onto it.
Then flip it over once it's already filled and that's how you get water into the whole thing.
Be very careful with the heat plate that...