Not easily, especially with 4-core cable. Without access to the conductor itself, you would have to calculate the temperature using thermal modelling techniques such as the Neher-McGrath or IEC 287 methods.
Basically, you calculate the heat generated by I2R losses in the conductor and shields, then calculate the temperature rise through the thermal resistance of the cable insulation and jacket.
Rating of Electric Power Cables by George J. Anders, IEEE Press, 1997 gives the theory and equations for calculating ampacity. Calculations for temperature rise could be developed using the same theoretical methods. Good luck.
On second thought, you might be able to calculate the resistance if you could measure sending end and receiving end voltage and current (including phase angles). Then measure the resistance of an unenergized cable at a known temperature. You could find the temperature with the equation:
T2 = R2*(T0 + T1)/R1 - T2
Where R2 is the resistance of the energized cable, R1 is the resistance of the unergized cable, T0 is 228 degC for aluminum or 234.5 degC for copper, T1 is the temperature of the unenergized cable, and T2 is the temperature of the energized cable.
You would have to use the resistance, not the impedance of the cable, thus the need to take phase angles into account in measuring voltages and current.
