The Jacob W. discussion is under the cases from the 80's threads, IIRC. I am sure the dogs used in the Jacob W. search would have been some sort of cadaver dogs. I was just amazed that they were still felt to be effective so long after! The search was being done by LE there on a farm, and they were digging up what was supposedly an area where ashes from a wood burning furnace have been dumped over the years. I have no clue whether that would help the dogs or make it more difficult for them.
Warning: explicit information about human remains follows.
I know it is amazingly difficult to completely burn a human body. Professional crematoriums use extremely high heat and then they run the results through a machine that pulverises them into particles of a certain maximum size (quite small) so that if the family decides to scatter the "cremains" (as they are called), they won't be freaked out by finding anything that is recognisably a bone or tooth fragment.
So if human remains were burned in that stove, I would expect there to be bone or tooth fragments. Once such fragments were spread in the environment, they would resume decomposing and would then give off a scent detectable by a HRD dog.
One interesting case I read about (but can't find the link for, sorry!) was a cadaver dog that alerted on a tree. Kept going back and alerting on this one tree. They checked the immediate area of the tree and couldn't find anything, so they chalked it up to a false alert by the dog.
Several months later, someone discovered remains coming out of the ground on the slope uphill of that tree. There had been rain and the soil above the body had eroded, exposing the remains.
When they took the dog back, it alerted on the tree again. Then as the handler encouraged the dog to work the rest of the area, the dog eventually alerted on the actual grave.
The theory was that the remains had decomposed and some of the products of decomposition had dissolved into the ground water, which moved downhill and was taken up by the tree.