I would try an energy method - look at the problem as one of breaking the crystals in the metal. In that view it is displacing at least the volume of penetration, from which one could determine the amount of energy to nearly liquefy a similar volume of metal.
Sensibly, if the material is already near the melting point, the force required lessens.
At each increment in depth there will be a volume of material intersected by the cone, so divide the energy required for that incremental amount by the distance required to get the force required for that increment. Since the volume incrementally displaced is the cube of the depth, the forces should be increasing at least as the cube of the depth with some factor for increasing friction; simple enough to test with a small setup and more limited depths.
The inaccuracy to this is that it doesn't account for residual strength in the displace material, and it doesn't include material outside the cone volume that is also displaced. It also avoids the contribution of elastic deformation outside the plastic zone and the friction between the cone and the material being displaced. Accounting for torque applied and thread friction is a separate issue.
I don't imagine the amounts from these contributors are equal to the initial volumetric displacement, so doubling the values from melting should be representative.
Altogether I would not expect a simple formula.
I would probably pre-drill the indentation, although since similar amounts of material are displaced, one could look at the power absorbed during the process to also make an estimate similar to melting the material.
