The concept of elastic dipole tensor of a defect is generalised to enable the treatment of lattice distortions, produced by defects at elevated temperatures. Thermodynamic and statistical mechanics derivations show the feasibility of computing the formation free energy and finite-temperature elastic dipole tensor of a $frac{1}{2}langle 111 rangle$ self-interstitial atom dislocation loop. The method exhibits good numerical stability even in the high temperature limit. Our derivation relates the discrete atomic and continuum representations of stress produced by defects, and hence the definition of elastic dipole tensor at finite temperature.