Waterbeds Go Tubular
 

Manufacturers responded with new designs and the open, bladder-type of waterbed mattress was replaced with a mattress featuring internal baffles that would mute the wave action of previous designs. Traditional waterbed mattresses needed a heating element to keep the water temperature as high or higher, than your normal body temperature.

Yes, they can climb on and sleep on a waterbed. The question you should be asking is ....Is there enough room left on the bed for a human to sleep after the fur-kids go to bed....