This is where convection gets involved. Heated water moves away from the heat source. If it isn't moving enough, you need more heat.if you have a single heat source under the middle, the edges may still freeze over,
The shape of the convection currents will depend on things like whether you use a point source, a ring around the perimeter, or an air cavity with a mostly uniform temperature of air. None of these things rely on heat sink grease. If the bucket doesn't absorb the applied heat fast enough, the temperature in a confined space will simply increase until it does. Simply put, equilibrium must happen eventually, and it doesn't take all day to do that.
I'm working with 30 years of experience as a State Certified thermodynamic designer and 10 years as a show dog breeder, but I don't feel compelled to micro-manage a dog water bucket. Just shove a heater under it and see if it's frozen in the morning. If fail, increase the energy input or the insulation on the bucket. If you want to listen to Doktor Jones, put some heat sink compound on the heater(s) and paint the bottom of the bucket. It won't hurt anything.
I don't know about this guy, but the Eskimos leave their dogs outside in the most horrid blizzards, so it's probably OK in the lower 48. IIRC, this is about a Labrador. They come equipped with fur coats and are large enough to have an energy surplus, most of the time. They are also smart enough to hide from the wind chill effect. I expect the dog will go in his dog house, hide under a mobile home or a car, or find a corner somewhere to curl up with his tail over his nose. If all else fails, they are smart enough to scratch at the door.Where is your DOG kept outside when it is freezing cold?