The short answer is nobody knows. There were no first-hand written accounts of the burial, and even legend is inconsistent in the matter.
It is quite likely there isn't any tomb to be found. Altaic peoples such as the Mongols often practiced open-air "burials"
When the right time had come, the corpse was usually placed on a cart
(tärgä) pulled by horse or cow. Then the bereaved men of the family
followed the cart to the clan's or family's burial place, which was an
uninhabited area separate from the areas used by the nomads. These
places were sacred and only visited for funeral-related events.
In other areas, especially in South Mongolia, the corpse was placed on
a horse's back and upon reaching the funeral site, the horse was urged
to gallop until the corpse was thrown off.
Some stones were put next to the head in order to recognize the burial
site later. Then a fire was made to sacrifice the select pieces of
(lamb) meat and white dishes (cagaan idää).
Depositing the corpse in the steppe was meant to sacrifice it to
predatory animals. According to Mongolians this is the last virtous
act a person can carry out. This idea is much older than Lamaism and
exhibits a really strong shamanistic element of spiritual thought.