I think you should start this by following the logic in the Neher–McGrath formula and work from there. Why reinvent the wheel?
This is from the handbook commentary in 310.15
A description of this calculation method was given in AIEE paper No. 5-660, “The Calculation of the Temperature Rise and Load Capability of Cable Systems,” by Neher and McGrath. This paper was presented to the AIEE general meeting in Montreal, Quebec, on June 24–28, 1956, and was published in AIEE Transactions, Part III (Power Apparatus and Systems), Vol. 76, October 1957, pp. 752–772. The AIEE (American Institute of Electrical Engineers) is now the Institute of Electrical and Electronics Engineers (IEEE).
You can probably find this paper on the net somewhere.