The crack-tip parameters, such asJ; T*, ΔT* etc, which quantify the severity of the stress/strain fields near the crack-tip in elastic-plastic materials subject to thermo-mechanical loading, are often expressed as integrals over a path that is infinitesimally close to the crack-tip (front). The integrand in such integrals involves the stress-working density, stress, strain and displacement fields arbitrarily close to the crack-tip. In a numerical analysis, such data near the crack-tip are not expected to be very accurate. This paper describes simple approaches and attendant computational algorithms, wherein, the "crack-tip integral" parameters may be evaluated through "equivalent domain integrals" (EDI) alone. It is also seen that the present (EDI) approaches form the generic basis for the popular "virtual crack extension" (VCE) methods. Several examples of thermo-mechanical fracture, including: (i) thermal loading of an elastic material, (ii) arbitrary loading/unloading/reloading of an elastic-plastic material, containing a single dominant crack, are presented to illustrate the present approach and its accuracy.