After a warm/hot prewash you want to soak the bones in a sink, bucket, bin, or other vessel with more hot, but not boiling water. Boiling bones can warp them or cause grease to seep into the bones and leave stains that may or may not come out during the whitening phase. Typically, unless you have a crazy water heater, you're fine just turning the water on full hot. Cool or cold water will do nothing for the degreasing process.

Dawn dish soap tends to be the preferred soad for degreasing. It's what they use to clean baby ducks during oil spills. I'm not sure how other soaps hold up, but Dawn is available at the dollar store ;) So I don't mind using half a bottle for one batch of bones.

You'll have to rinse, scrub, and change the water several times, I usually let them soak for 2-3 hours (or as long as it takes for the water to get room temperature) Each time you rinse you will need to replace the water and soap entirely. I only use 4-5 squeezes each time I fill the sink. It's also a great idea to manually work grease and flesh debris off each time you change the water, especially with joint pieces, like that femur, which can have traces of cartilage on them. Another thing to watch for with skulls is teeth. They will be falling out as the water softens the gum tissue. You don't want to loose these, so I suggest pulling them out as soon as they get loose.

(I should've taken some before shots, you can see in these photos the water is discolored/dingy)

Do this several times, at least 6-7 but depending on the condition of your bones you may need to do this more. Some people do this process for weeks.