Deformation of Heated Transmission Cable in a Conduit
This isn't a direct answer to the question of "calculate the deformation of cable due to thermal expansion", but rather an attempt at a practical solution.

Firstly, I have sketched my understanding of the problem below.



I have seen piping designs where long, straight sections of pipe have U-shaped sections inserted to account for thermal expansion of the pipework. The expansion is taken up by flexing of the U-parts.



Depending on the bending radius of your cable it may be possible to solve your problem in a similar way. Insert an intentional bend in the cable every few hundred meters. Thermal expansion would be taken up by expansion/contraction of the bend. 



A practical design is likely to require cable pits at 100-200m intervals. These cable pits are required to pull the cable through in stages, so the pull tension is kept low enough. (Pulling 2,000 ft. = 600 metres of cable at once would likely require an excessive pulling tension, which would damage the cable by elongation.)

Your problem may be practically solved by putting bends in these pits, allowing for thermal expansion in specific places where you have designed to allow it.

A full loop of cable would probably require an excessively large pit. A few shallower bends would likely be suffficient - see below.



Regularly spaced "expansion pits" would be analogous to putting expansion joints in concrete slabs, to allow expansion of the concrete.



Edit:


Assume copper cable.
Assume the cable's length is determined by thermal expansion of the
copper conductor. (Disregard the thermal expansion of the XLPE
plastic insulation.)
Assume the cable temperature varies from 25 C (ambient) to 90 C
(upper limit for XLPE) so that \$ \Delta T = 65^{\circ} C \$.
The linear thermal co-efficient of expansion of copper is \$ 16.6 \times 10^{-6} 
   m_{expansion} / ( m_{original length} . ^{\circ} C ) \$ .


Then the thermal expansion of a 600m length of cable will be approximately \$ 1.66 \times 10^{-6} \times 600 m \times 65^{\circ} C \approx 70cm \$, which seems modest enough. It could be absorbed by allowing for 20cm expansion in each of four cable pits along the route.