The question I have most likely is best answered by a member with a geologist's background....

We are endeavouring to predict temperature gradients sub surface for the following conditions:-

1)  Hole depth:  5000 metres

2) Cased hole section size:  9 5/8in.

3) Hole diameter:  8 1/2in.

4) Water depth:  4000m - 4500m

Clearly, this is a deep ocean mining operation.  Being well away from the edge of the Ocean Margin of the continental shelf, we do not anticipate any sedimentary layer,  normally encountered at the mudline on continential shelves.  Further, it is advised that no well control provisions need to be considered in well construction.  

Temperature gradients are well documented for deep hole oil & gas exploration wells (HP/HT), but the underlying question here is since there is no expectation of encountering any formations towards terminal depth of the well (TD), can serious upward temperature gradients by anticipated?